EBK COLLEGE ALGEBRA
6th Edition
ISBN: 9780100802797
Author: Dugopolski
Publisher: YUZU
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Textbook Question
Chapter 2.3, Problem 34E
Match each function in Exercises 27– 34 with its graph (a)-(h). See the procedure for multiple transformations on page 214.
y = –2(x – 4)2 – 2
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Chapter 2 Solutions
EBK COLLEGE ALGEBRA
Ch. 2.1 -
True or False? Explain.
1. Any set of ordered...Ch. 2.1 - True or False? Explain. If f = {(1, 1), (2, 4),...Ch. 2.1 -
True or False? Explain.
3. The domain of f(x) =...Ch. 2.1 - True or False? Explain. Each student’s exam grade...Ch. 2.1 -
True or False? Explain.
5. If f(x) = x2, then...Ch. 2.1 - Prob. 6FTCh. 2.1 - True or False? Explain. The range of y = 8 – x2 is...Ch. 2.1 - Prob. 8FTCh. 2.1 - True or False? Explain.
9. If then f(0) = –1.
Ch. 2.1 - Prob. 10FT
Ch. 2.1 -
Fill in the blank.
1. If the value of m is...Ch. 2.1 - Prob. 2ECh. 2.1 -
Fill in the blank.
3. Any set of ordered pairs is...Ch. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - For each pair of variables determine whether a is...Ch. 2.1 -
For each pair of variables determine whether a...Ch. 2.1 - For each pair of variables determine whether a is...Ch. 2.1 - For each pair of variables determine whether a is...Ch. 2.1 - For each pair of variables determine whether a is...Ch. 2.1 - For each pair of variables determine whether a is...Ch. 2.1 - For each pair of variables determine whether a is...Ch. 2.1 - For each pair of variables determine whether a is...Ch. 2.1 - For each pair of variables determine whether a is...Ch. 2.1 - For each pair of variables determine whether a is...Ch. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Determine whether each relation is a function....Ch. 2.1 - Determine whether each relation is a function.
26....Ch. 2.1 - Determine whether each relation is a function....Ch. 2.1 - Determine whether each relation is a function. { (...Ch. 2.1 -
Determine whether each relation is a...Ch. 2.1 - Determine whether each relation is a function.Ch. 2.1 -
Determine whether each relation is a...Ch. 2.1 - Determine whether each relation is a function.Ch. 2.1 - Determine whether each equation defines y as a...Ch. 2.1 -
Determine whether each equation defines y as a...Ch. 2.1 -
Determine whether each equation defines y as a...Ch. 2.1 -
Determine whether each equation defines y as a...Ch. 2.1 - Determine whether each equation defines y as a...Ch. 2.1 -
Determine whether each equation defines y as a...Ch. 2.1 - Determine whether each equation defines y as a...Ch. 2.1 - Determine whether each equation defines y as a...Ch. 2.1 - Determine whether each equation defines y as a...Ch. 2.1 - Determine whether each equation defines y as a...Ch. 2.1 -
Determine whether each equation defines y as a...Ch. 2.1 - Determine whether each equation defines y as a...Ch. 2.1 - Determine the domain and range of each relation....Ch. 2.1 - Determine the domain and range of each relation....Ch. 2.1 - Determine the domain and range of each relation....Ch. 2.1 - Determine the domain and range of each relation....Ch. 2.1 - Determine the domain and range of each relation....Ch. 2.1 -
Determine the domain and range of each relation....Ch. 2.1 -
Determine the domain and range of each relation....Ch. 2.1 - Prob. 52ECh. 2.1 -
Determine the domain and range of each relation....Ch. 2.1 - Prob. 54ECh. 2.1 - Prob. 55ECh. 2.1 - Prob. 56ECh. 2.1 -
Let f = {(2, 6), (3, 8), (4, 5)} and g(x) = 3x +...Ch. 2.1 -
Let f = {(2, 6), (3, 8), (4, 5)} and g(x) = 3x +...Ch. 2.1 -
Let f = {(2, 6), (3, 8), (4, 5)} and g(x) = 3x +...Ch. 2.1 - Let f = {(2, 6), (3, 8), (4, 5)} and g(x) = 3x +...Ch. 2.1 - Let f = {(2, 6), (3, 8), (4, 5)} and g(x) = 3x +...Ch. 2.1 -
Let f = {(2, 6), (3, 8), (4, 5)} and g(x) = 3x +...Ch. 2.1 -
Let f = {(2, 6), (3, 8), (4, 5)} and g(x) = 3x +...Ch. 2.1 -
Let f = {(2, 6), (3, 8), (4, 5)} and g(x) = 3x +...Ch. 2.1 -
Let f = {(2, 6), (3, 8), (4, 5)} and g(x) = 3x +...Ch. 2.1 -
Let f = {(2, 6), (3, 8), (4, 5)} and g(x) = 3x +...Ch. 2.1 - Let f(x) = 3x2– x and g(x) = 4x – 2. Find the...Ch. 2.1 -
Let f(x) = 3x2 – x and g(x) = 4x – 2. Find the...Ch. 2.1 -
Let f(x) = 3x2 – x and g(x) = 4x – 2. Find the...Ch. 2.1 - Let f(x) = 3x2– x and g(x) = 4x – 2. Find the...Ch. 2.1 -
Let f(x) = 3x2 – x and g(x) = 4x – 2. Find the...Ch. 2.1 - Prob. 72ECh. 2.1 -
Let f(x) = 3x2 – x and g(x) = 4x – 2. Find the...Ch. 2.1 - Prob. 74ECh. 2.1 - Let f(x) = 3x2– x and g(x) = 4x – 2. Find the...Ch. 2.1 - Let f(x) = 3x2– x and g(x) = 4x – 2. Find the...Ch. 2.1 - Let f(x) = 3x2– x and g(x) = 4x – 2. Find the...Ch. 2.1 -
Let f(x) = 3x2 – x and g(x) = 4x – 2. Find the...Ch. 2.1 - The following problems involve average rate of...Ch. 2.1 -
The following problems involve average rate of...Ch. 2.1 -
The following problems involve average rate of...Ch. 2.1 -
The following problems involve average rate of...Ch. 2.1 - The following problems involve average rate of...Ch. 2.1 - Prob. 84ECh. 2.1 - Find the difference quotient for each function and...Ch. 2.1 - Prob. 86ECh. 2.1 - Find the difference quotient for each function...Ch. 2.1 - Find the difference quotient for each function and...Ch. 2.1 -
Find the difference quotient for each function...Ch. 2.1 - Find the difference quotient for each function...Ch. 2.1 - Find the difference quotient for each function...Ch. 2.1 - Prob. 92ECh. 2.1 - Prob. 93ECh. 2.1 - Prob. 94ECh. 2.1 - Prob. 95ECh. 2.1 - Prob. 96ECh. 2.1 - Prob. 97ECh. 2.1 - Prob. 98ECh. 2.1 - Prob. 99ECh. 2.1 - Prob. 100ECh. 2.1 - Solve each problem.
101. Constructing Functions...Ch. 2.1 - Prob. 102ECh. 2.1 - Prob. 103ECh. 2.1 - Prob. 104ECh. 2.1 - Prob. 105ECh. 2.1 - Prob. 106ECh. 2.1 - Prob. 107ECh. 2.1 - Prob. 108ECh. 2.1 - Solve each problem. Concert Revenue The revenue in...Ch. 2.1 - Prob. 110ECh. 2.1 - Prob. 111ECh. 2.1 - Prob. 112ECh. 2.1 - Prob. 113ECh. 2.1 - Prob. 114ECh. 2.1 - Prob. 115ECh. 2.1 - Prob. 116ECh. 2.1 - Prob. 117ECh. 2.1 - Prob. 118ECh. 2.1 - Prob. 119ECh. 2.1 -
120. Swim Meet Two swimmers of unequal ability...Ch. 2.1 - Is the radius of a circle a function of its area?Ch. 2.1 - Prob. 2PQCh. 2.1 - Prob. 3PQCh. 2.1 - Prob. 4PQCh. 2.1 - Prob. 5PQCh. 2.1 - Prob. 6PQCh. 2.1 - Prob. 7PQCh. 2.1 - Prob. 8PQCh. 2.1 - 9. Find and simplify the difference quotient for...Ch. 2.1 - Prob. LCCh. 2.2 - FOR THOUGHT... True or False? Explain
1. The range...Ch. 2.2 - Prob. 2FTCh. 2.2 - FOR THOUGHT... True or False? Explain
3. The...Ch. 2.2 - Prob. 4FTCh. 2.2 - Prob. 5FTCh. 2.2 - Prob. 6FTCh. 2.2 - Prob. 7FTCh. 2.2 - Prob. 8FTCh. 2.2 - Prob. 9FTCh. 2.2 - FOR THOUGHT... True or False? Explain The function...Ch. 2.2 - Fill in the blank. The function is the ______...Ch. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - Prob. 5ECh. 2.2 - Prob. 6ECh. 2.2 - Make a table listing ordered pairs that satisfy...Ch. 2.2 - Prob. 8ECh. 2.2 - Make a table listing ordered pairs that satisfy...Ch. 2.2 - Make a table listing ordered pairs that satisfy...Ch. 2.2 - Make a table listing ordered pairs that satisfy...Ch. 2.2 - Prob. 12ECh. 2.2 - Make a table listing ordered pairs that satisfy...Ch. 2.2 - Prob. 14ECh. 2.2 - Make a table listing ordered pairs that satisfy...Ch. 2.2 - Make a table listing ordered pairs that satisfy...Ch. 2.2 -
Make a table listing ordered pairs that satisfy...Ch. 2.2 - Prob. 18ECh. 2.2 - Make a table listing ordered pairs that satisfy...Ch. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 -
Make a table listing ordered pairs that satisfy...Ch. 2.2 - Make a table listing ordered pairs that satisfy...Ch. 2.2 - Prob. 24ECh. 2.2 - Make a table listing ordered pairs that satisfy...Ch. 2.2 -
Make a table listing ordered pairs that satisfy...Ch. 2.2 - Make a table listing ordered pairs that satisfy...Ch. 2.2 - Make a table listing ordered pairs that satisfy...Ch. 2.2 -
Make a table listing ordered pairs that satisfy...Ch. 2.2 - Prob. 30ECh. 2.2 - Make a table listing ordered pairs that satisfy...Ch. 2.2 - Prob. 32ECh. 2.2 - Prob. 33ECh. 2.2 - Make a table listing ordered pairs that satisfy...Ch. 2.2 - Prob. 35ECh. 2.2 - Prob. 36ECh. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 -
Make a table listing ordered pairs for each...Ch. 2.2 - Make a table listing ordered pairs for each...Ch. 2.2 -
Make a table listing ordered pairs for each...Ch. 2.2 - Make a table listing ordered pairs for each...Ch. 2.2 - Make a table listing ordered pairs for each...Ch. 2.2 -
Make a table listing ordered pairs for each...Ch. 2.2 -
Make a table listing ordered pairs for each...Ch. 2.2 -
Make a table listing ordered pairs for each...Ch. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Prob. 49ECh. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.2 - Prob. 52ECh. 2.2 - From the graph of each function in Exercises 53–...Ch. 2.2 - Prob. 54ECh. 2.2 - From the graph of each function in Exercises 53–...Ch. 2.2 - Prob. 56ECh. 2.2 - Prob. 57ECh. 2.2 - From the graph of each function in Exercises 53–...Ch. 2.2 -
From the graph of each function in Exercises...Ch. 2.2 - Prob. 60ECh. 2.2 - Prob. 61ECh. 2.2 - Prob. 62ECh. 2.2 - Prob. 63ECh. 2.2 - Prob. 64ECh. 2.2 - Make a table listing ordered pairs for each...Ch. 2.2 - Prob. 66ECh. 2.2 - Prob. 67ECh. 2.2 - Prob. 68ECh. 2.2 - Prob. 69ECh. 2.2 - Prob. 70ECh. 2.2 - Make a table listing ordered pairs for each...Ch. 2.2 - Prob. 72ECh. 2.2 - Prob. 73ECh. 2.2 - Prob. 74ECh. 2.2 - Write a piecewise function for each given graph.Ch. 2.2 - Prob. 76ECh. 2.2 - Prob. 77ECh. 2.2 - Prob. 78ECh. 2.2 - Prob. 79ECh. 2.2 - Prob. 80ECh. 2.2 - Prob. 81ECh. 2.2 - Prob. 82ECh. 2.2 - Prob. 83ECh. 2.2 - Prob. 84ECh. 2.2 - Prob. 85ECh. 2.2 - Prob. 86ECh. 2.2 - Prob. 87ECh. 2.2 - Prob. 88ECh. 2.2 - Prob. 89ECh. 2.2 - Prob. 90ECh. 2.2 - Draw a graph that pictures each situation. Explain...Ch. 2.2 - Prob. 92ECh. 2.2 - Prob. 93ECh. 2.2 -
Draw a graph that pictures each situation....Ch. 2.2 - Prob. 95ECh. 2.2 - Prob. 96ECh. 2.2 - Prob. 97ECh. 2.2 - Prob. 98ECh. 2.2 - Prob. 99ECh. 2.2 - Prob. 100ECh. 2.2 - Prob. 101ECh. 2.2 - Prob. 102ECh. 2.2 - Prob. 103ECh. 2.2 - Prob. 104ECh. 2.2 - Prob. 105ECh. 2.2 - Prob. 106ECh. 2.2 - Prob. 107ECh. 2.2 - Prob. 108ECh. 2.2 - Factor completely. a. w4 – 1 b. 10a3 + 3a2 – 18aCh. 2.2 - Prob. 110ECh. 2.2 - Best-Fitting Pipe A work crew is digging a...Ch. 2.2 - Prob. 112ECh. 2.2 - Prob. 1PQCh. 2.2 - Prob. 2PQCh. 2.2 - Prob. 3PQCh. 2.2 - Prob. 4PQCh. 2.2 - Prob. 5PQCh. 2.2 -
LINKING concepts...
For Individual or Group...Ch. 2.3 - FOR THOUGHT... True or False? Explain. The graph...Ch. 2.3 - Prob. 2FTCh. 2.3 - Prob. 3FTCh. 2.3 - Prob. 4FTCh. 2.3 - Prob. 5FTCh. 2.3 - FOR THOUGHT... True or False? Explain.
6. The...Ch. 2.3 - Prob. 7FTCh. 2.3 - Prob. 8FTCh. 2.3 - Prob. 9FTCh. 2.3 - Prob. 10FTCh. 2.3 - Prob. 1ECh. 2.3 - Prob. 2ECh. 2.3 - Fill in the blank. The graph of a function of the...Ch. 2.3 - Prob. 4ECh. 2.3 - Fill in the blank. The graph of y = – f(x) is a(n)...Ch. 2.3 - Prob. 6ECh. 2.3 - Fill in the blank.
7. The function f(x) = mx + b...Ch. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Sketch the graphs of each pair of functions on the...Ch. 2.3 - Sketch the graphs of each pair of functions on the...Ch. 2.3 - Sketch the graphs of each pair of functions on the...Ch. 2.3 - Sketch the graphs of each pair of functions on the...Ch. 2.3 - Sketch the graphs of each pair of functions on the...Ch. 2.3 - Prob. 16ECh. 2.3 -
Sketch the graphs of each pair of functions on...Ch. 2.3 - Prob. 18ECh. 2.3 -
Sketch the graphs of each pair of functions on...Ch. 2.3 -
Sketch the graphs of each pair of functions on...Ch. 2.3 - Sketch the graphs of each pair of functions on the...Ch. 2.3 - Prob. 22ECh. 2.3 - Sketch the graphs of each pair of functions on the...Ch. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 -
Match each function in Exercises 27–34 with its...Ch. 2.3 -
Match each function in Exercises 27–34 with its...Ch. 2.3 - Match each function in Exercises 27– 34 with its...Ch. 2.3 -
Match each function in Exercises 27–34 with its...Ch. 2.3 -
Match each function in Exercises 27–34 with its...Ch. 2.3 - Match each function in Exercises 27– 34 with its...Ch. 2.3 -
Match each function in Exercises 27–34 with its...Ch. 2.3 - Match each function in Exercises 27– 34 with its...Ch. 2.3 -
Write the equation of each graph after the...Ch. 2.3 - Prob. 36ECh. 2.3 - Write the equation of each graph after the...Ch. 2.3 - Write the equation of each graph after the...Ch. 2.3 -
Write the equation of each graph after the...Ch. 2.3 - Write the equation of each graph after the...Ch. 2.3 - Write the equation of each graph after the...Ch. 2.3 -
Write the equation of each graph after the...Ch. 2.3 - Write the equation of each graph after the...Ch. 2.3 -
Write the equation of each graph after the...Ch. 2.3 - Use transformations to graph each function and...Ch. 2.3 - Use transformations to graph each function and...Ch. 2.3 - Use transformations to graph each function and...Ch. 2.3 - Prob. 48ECh. 2.3 - Use transformations to graph each function and...Ch. 2.3 - Prob. 50ECh. 2.3 - Prob. 51ECh. 2.3 - Prob. 52ECh. 2.3 - Use transformations to graph each function and...Ch. 2.3 - Use transformations to graph each function and...Ch. 2.3 - Use transformations to graph each function and...Ch. 2.3 - Use transformations to graph each function and...Ch. 2.3 - Use transformations to graph each function and...Ch. 2.3 - Use transformations to graph each function and...Ch. 2.3 - Use transformations to graph each function and...Ch. 2.3 - Use transformations to graph each function and...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Determine algebraically whether the function is...Ch. 2.3 - Match each function with its graph (a)-(h). y = 2...Ch. 2.3 - Match each function with its graph (a)-(h).Ch. 2.3 - Match each function with its graph (a)-(h).
83....Ch. 2.3 - Match each function with its graph (a)-(h).
84....Ch. 2.3 - Match each function with its graph (a)-(h).
85....Ch. 2.3 - Match each function with its graph (a)-(h).
86....Ch. 2.3 - Match each function with its graph (a)-(h).
87....Ch. 2.3 - Match each function with its graph (a)-(h).
88....Ch. 2.3 - Solve each inequality by reading the corresponding...Ch. 2.3 - Solve each inequality by reading the corresponding...Ch. 2.3 - Solve each inequality by reading the corresponding...Ch. 2.3 - Solve each inequality by reading the corresponding...Ch. 2.3 - Solve each inequality by graphing an appropriate...Ch. 2.3 - Prob. 94ECh. 2.3 - Prob. 95ECh. 2.3 - Prob. 96ECh. 2.3 - Prob. 97ECh. 2.3 - Solve each inequality by graphing an appropriate...Ch. 2.3 - Prob. 99ECh. 2.3 - Prob. 100ECh. 2.3 - Prob. 101ECh. 2.3 - Prob. 102ECh. 2.3 -
Graph each of the following functions by...Ch. 2.3 -
Graph each of the following functions by...Ch. 2.3 - Prob. 105ECh. 2.3 - Solve each problem. Cost-of-Living Raise Each...Ch. 2.3 - Prob. 107ECh. 2.3 - Prob. 108ECh. 2.3 - Prob. 109ECh. 2.3 - Prob. 110ECh. 2.3 - Prob. 111ECh. 2.3 - Prob. 112ECh. 2.3 - Prob. 113ECh. 2.3 - Prob. 114ECh. 2.3 - Prob. 115ECh. 2.3 - Prob. 116ECh. 2.3 - Prob. 117ECh. 2.3 - Prob. 118ECh. 2.3 - Prob. 1PQCh. 2.3 - Prob. 2PQCh. 2.3 - Prob. 3PQCh. 2.3 - Prob. 4PQCh. 2.3 - 5. If the curve y = x2 is translated 6 units to...Ch. 2.3 - Prob. 6PQCh. 2.3 - LINKING concepts... For Individual or Group...Ch. 2.4 - True or False? Explain.
1. If f = {(2, 4)} and g =...Ch. 2.4 - True or False? Explain. If f = { ( 1 , 6 ) , ( 9 ,...Ch. 2.4 - Prob. 3FTCh. 2.4 - Prob. 4FTCh. 2.4 - Prob. 5FTCh. 2.4 - Prob. 6FTCh. 2.4 - True or False? Explain. If f(x) x and g ( x ) = x...Ch. 2.4 - Prob. 8FTCh. 2.4 - True or False? Explain.
9. If F(x) = (x –9)2, g(x)...Ch. 2.4 - Prob. 10FTCh. 2.4 - Prob. 1ECh. 2.4 - Prob. 2ECh. 2.4 - Fill in the blank.
3. For two functions f and g,...Ch. 2.4 - Fill in the blank. For two functions f and g, the...Ch. 2.4 - Fill in the blank.
5. If f and g are functions,...Ch. 2.4 - Prob. 6ECh. 2.4 - Let f(x) = x – 3 and g(x) = x2– x. Find and...Ch. 2.4 - Let f(x) = x – 3 and g(x) = x2–x. Find and...Ch. 2.4 - Let f(x) = x – 3 and g(x) = x2– x. Find and...Ch. 2.4 - Let f(x) = x – 3 and g(x) = x2– x. Find and...Ch. 2.4 - Let f(x) = x – 3 and g(x) = x2–x. Find and...Ch. 2.4 - Let f(x) = x – 3 and g(x) = x2– x. Find and...Ch. 2.4 - Let f(x) =x–3 and g(x) = x2– x. Find and simplify...Ch. 2.4 - Let f(x) = x – 3 and g(x) = x2– x. Find and...Ch. 2.4 - Let f(x) = x – 3 and g(x) = x2– x. Find and...Ch. 2.4 - Let f(x) = x – 3 and g(x) = x2– x. Find and...Ch. 2.4 - Let f(x) = x –3 and g(x) = x2 – x. Find and...Ch. 2.4 - Let f(x) = x –3 andg(x) = x2 – x. Find and...Ch. 2.4 - Define the functions f, g, and h as follows: f=...Ch. 2.4 - Define the functions f, g, and h as follows: f=...Ch. 2.4 - Define the functions f, g, and h as follows: f=...Ch. 2.4 - Define the functions f, g, and h as follows:
f=...Ch. 2.4 - Define the functions f, g, and h as follows: f=...Ch. 2.4 - Define the functions f, g, and h as follows:
f=...Ch. 2.4 - Define the functions f, g, and h as follows: f=...Ch. 2.4 - Define the functions f, g, and h as follows:
f=...Ch. 2.4 - Let , and .Find an equation defining each...Ch. 2.4 - Let f ( x ) = x , g ( x ) = x − 4 , and h ( x ) =...Ch. 2.4 - Let , and . Find an equation defining each...Ch. 2.4 - Let f ( x ) = x , g ( x ) = x − 4 , and h ( x ) =...Ch. 2.4 - Let , and .Find an equation defining each...Ch. 2.4 - Le f ( x ) = x , g ( x ) = x − 4 , and h ( x ) = 1...Ch. 2.4 - Let , and . Find an equation defining each...Ch. 2.4 - Let f ( x ) = x , g ( x ) = x − 4 , and h ( x ) =...Ch. 2.4 - Define the functions f, g, and h as follows: f=...Ch. 2.4 - Define the functions f, g, and h as follows:
f=...Ch. 2.4 - Define the functions f, g, and h as follows:...Ch. 2.4 - Define the functions f, g, and h as follows:...Ch. 2.4 - Define the functions f, g, and h as...Ch. 2.4 - Define the functions f, g, and h as follows:...Ch. 2.4 - Let f(x) = 3x – 1, g(x) = x2 + 1 and h(x) =. x + 1...Ch. 2.4 - Let f(x) = 3x – 1, g(x) = x2 + 1 and h(x) =. x + 1...Ch. 2.4 - Let f(x) = 3x – 1, g(x) = x2 + 1 and. Evaluate...Ch. 2.4 - Let f(x) = 3x – 1, g(x) = x2 + 1 and. Evaluate...Ch. 2.4 - Let f(x) = 3x –1, g(x) = x2 + 1 and . Evaluate...Ch. 2.4 - Let f(x) = 3x –1, g(x) = x2 + 1 and . Evaluate...Ch. 2.4 - Let f(x) = 3x – 1, g(x) = x2 + 1 and. Evaluate...Ch. 2.4 - Let f(x) = 3x – 1, g(x) = x2 + 1 and. Evaluate...Ch. 2.4 - Let f(x) = 3x –1, g(x) = x2 + 1 and . Evaluate...Ch. 2.4 - Let f(x) = 3x –1, g(x) = x2 + 1 and . Evaluate...Ch. 2.4 - Let f(x) = 3x – 1, g(x) = x2 + 1 and . Evaluate...Ch. 2.4 - Prob. 52ECh. 2.4 - Let f(x) = 3x –1, g(x) = x2 + 1 and . Evaluate...Ch. 2.4 - Prob. 54ECh. 2.4 - Let f(x) = x – 2, g(x) =and h(x) =. Find an...Ch. 2.4 - Let f(x) = x – 2, g(x) =and h(x) =. Find an...Ch. 2.4 - Prob. 57ECh. 2.4 - Prob. 58ECh. 2.4 - Let f ( x ) = x − 2 , g ( x ) = x , and h ( x ) =...Ch. 2.4 - Prob. 60ECh. 2.4 - Let f(x) = x – 2, g(x) =and . Find an equation...Ch. 2.4 - Prob. 62ECh. 2.4 - Prob. 63ECh. 2.4 - Prob. 64ECh. 2.4 - Prob. 65ECh. 2.4 - Prob. 66ECh. 2.4 - Let f(x) = |x|, g(x) = x – 7, and h(x) = x2. Write...Ch. 2.4 - Prob. 68ECh. 2.4 - Prob. 69ECh. 2.4 - Let f(x) = |x|, g(x) = x –7, and h(x)= x2. Write...Ch. 2.4 - Let f(x) = |x|, g(x) = x –7, and h(x) = x2. Write...Ch. 2.4 - Let f(x) = |x|, g(x) = x –7, and h(x) = x2. Write...Ch. 2.4 - Prob. 73ECh. 2.4 - Prob. 74ECh. 2.4 - Prob. 75ECh. 2.4 - Prob. 76ECh. 2.4 - Prob. 77ECh. 2.4 - For each given function f(x), find two functions...Ch. 2.4 - For each given function f(x), find two functions...Ch. 2.4 - Prob. 80ECh. 2.4 - For each given function f(x), find two functions...Ch. 2.4 - Prob. 82ECh. 2.4 - Prob. 83ECh. 2.4 - Prob. 84ECh. 2.4 - Prob. 85ECh. 2.4 - Prob. 86ECh. 2.4 - Prob. 87ECh. 2.4 - Prob. 88ECh. 2.4 - Use the two given functions to write y as a...Ch. 2.4 - Prob. 90ECh. 2.4 - Find each function from the given verbal...Ch. 2.4 - Prob. 92ECh. 2.4 - Prob. 93ECh. 2.4 - Prob. 94ECh. 2.4 - Prob. 95ECh. 2.4 - Prob. 96ECh. 2.4 - Prob. 97ECh. 2.4 - Prob. 98ECh. 2.4 - Prob. 99ECh. 2.4 - Prob. 100ECh. 2.4 - Prob. 101ECh. 2.4 - Prob. 102ECh. 2.4 - Prob. 103ECh. 2.4 - Solve each problem.
104. Profit The revenue in...Ch. 2.4 - Solve each problem.
105. Write the area A of a...Ch. 2.4 - Solve each problem. Write the perimeter of a...Ch. 2.4 - Solve each problem. Deforestation in Nigeria In...Ch. 2.4 - Prob. 108ECh. 2.4 - Prob. 109ECh. 2.4 - Prob. 110ECh. 2.4 - Prob. 111ECh. 2.4 - Prob. 112ECh. 2.4 - Prob. 113ECh. 2.4 - Prob. 114ECh. 2.4 - Prob. 115ECh. 2.4 - Prob. 116ECh. 2.4 - Prob. 117ECh. 2.4 - Prob. 118ECh. 2.4 - Prob. 119ECh. 2.4 - Prob. 120ECh. 2.4 - Prob. 121ECh. 2.4 - Prob. 122ECh. 2.4 - Prob. 123ECh. 2.4 - Prob. 124ECh. 2.4 - Prob. 125ECh. 2.4 - Prob. 126ECh. 2.4 - Prob. 1PQCh. 2.4 - Prob. 2PQCh. 2.4 - Prob. 3PQCh. 2.4 - Prob. 4PQCh. 2.4 - Prob. 5PQCh. 2.4 - Prob. 6PQCh. 2.4 - Prob. 7PQCh. 2.4 - Prob. 8PQCh. 2.4 - Prob. 9PQCh. 2.4 - Prob. LCCh. 2.5 - True or False? Explain.
1. The inverse of the...Ch. 2.5 - True or False? Explain. The function f(x) = –2 is...Ch. 2.5 - Prob. 3FTCh. 2.5 - Prob. 4FTCh. 2.5 - Prob. 5FTCh. 2.5 - Prob. 6FTCh. 2.5 - Prob. 7FTCh. 2.5 - Prob. 8FTCh. 2.5 - True or False? Explain.
9. According to the...Ch. 2.5 - Prob. 10FTCh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Determine whether each function is one-to-one....Ch. 2.5 - Determine whether each function is one-to-one....Ch. 2.5 - Determine whether each function is one-to-one....Ch. 2.5 - Determine whether each function is one-to-one....Ch. 2.5 - Determine whether each function is one-to-one....Ch. 2.5 - Determine whether each function is one-to-one....Ch. 2.5 - Use the horizontal line test to determine whether...Ch. 2.5 - Use the horizontal line test to determine whether...Ch. 2.5 - Use the horizontal line test to determine whether...Ch. 2.5 - Use the horizontal line test to determine whether...Ch. 2.5 - Use the horizontal line test to determine whether...Ch. 2.5 - Use the horizontal line test to determine whether...Ch. 2.5 - Determine whether each function is one-to-one.
19....Ch. 2.5 - Determine whether each function is one-to-one. h (...Ch. 2.5 - Determine whether each function is one-to-one.Ch. 2.5 - Determine whether each function is one-to-one.
22....Ch. 2.5 - Determine whether each function is one-to-one.
23....Ch. 2.5 - Determine whether each function is one-to-one. r (...Ch. 2.5 - Determine whether each function is one-to-one.
25....Ch. 2.5 - Determine whether each function is one-to-one.
26....Ch. 2.5 - Determine whether each function is one-to-one.
27....Ch. 2.5 - Determine whether each function is one-to-one.Ch. 2.5 - Determine whether each function is invertible. If...Ch. 2.5 - Determine whether each function is invertible. If...Ch. 2.5 - Determine whether each function is invertible. If...Ch. 2.5 - Determine whether each function is invertible. If...Ch. 2.5 - Determine whether each function is invertible. If...Ch. 2.5 - Prob. 34ECh. 2.5 - Determine whether each function is invertible. If...Ch. 2.5 - Prob. 36ECh. 2.5 - Determine whether each function is invertible and...Ch. 2.5 - Determine whether each function is invertible and...Ch. 2.5 - Prob. 39ECh. 2.5 - Prob. 40ECh. 2.5 - Prob. 41ECh. 2.5 - Prob. 42ECh. 2.5 - For each function f find
43.
Ch. 2.5 - Prob. 44ECh. 2.5 - Prob. 45ECh. 2.5 - Prob. 46ECh. 2.5 - Prob. 47ECh. 2.5 - Prob. 48ECh. 2.5 - Prob. 49ECh. 2.5 - Prob. 50ECh. 2.5 - Find the inverse of each function by reversing a...Ch. 2.5 - Find the inverse of each function by reversing a...Ch. 2.5 - Determine whether each pair of functions f and g...Ch. 2.5 - Determine whether each pair of functions f and g...Ch. 2.5 - Determine whether each pair of functions f and g...Ch. 2.5 - Determine whether each pair of functions f and g...Ch. 2.5 - For each function f sketch the graph of f–1.Ch. 2.5 - For each function f sketch the graph of f–1.Ch. 2.5 - For each function f sketch the graph of f–1.
59....Ch. 2.5 - For each function f sketch the graph of f–1.Ch. 2.5 - Find the inverse of each function and graph both f...Ch. 2.5 - Find the inverse of each function and graph both f...Ch. 2.5 - Find the inverse of each function and graph both f...Ch. 2.5 - Find the inverse of each function and graph both f...Ch. 2.5 - Find the inverse of each function and graph both f...Ch. 2.5 - Find the inverse of each function and graph both f...Ch. 2.5 - Find the inverse of each function and graph both f...Ch. 2.5 - Find the inverse of each function and graph both f...Ch. 2.5 - Find the inverse of each function using the...Ch. 2.5 - Find the inverse of each function using the...Ch. 2.5 - Find the inverse of each function using the...Ch. 2.5 - Find the inverse of each function using the...Ch. 2.5 - Find the inverse of each function using the...Ch. 2.5 - Find the inverse of each function using the...Ch. 2.5 - Find the inverse of each function using the...Ch. 2.5 - Find the inverse of each function using the...Ch. 2.5 - Find the inverse of each function using the...Ch. 2.5 - Find the inverse of each function using the...Ch. 2.5 - Find the inverse of each function using the...Ch. 2.5 - Find the inverse of each function using the...Ch. 2.5 - Find the inverse of each function using the...Ch. 2.5 - Find the inverse of each function using the...Ch. 2.5 - In each case find f(g(x)) and g(f(x)). Then...Ch. 2.5 - In each case find f(g(x)) and g(f(x)). Then...Ch. 2.5 - In each case find f(g(x)) and g(f(x)). Then...Ch. 2.5 - In each case find f(g(x)) and g(f(x)). Then...Ch. 2.5 - In each case find f(g(x)) and g(f(x)). Then...Ch. 2.5 - In each case find f(g(x)) and g(f(x)). Then...Ch. 2.5 - Prob. 89ECh. 2.5 - Prob. 90ECh. 2.5 - Prob. 91ECh. 2.5 - Prob. 92ECh. 2.5 - Solve each problem.
93. Price of a Car The tax on...Ch. 2.5 - Prob. 94ECh. 2.5 - Prob. 95ECh. 2.5 - Solve each problem. Temperature The function...Ch. 2.5 - Solve each problem. Landing Speed The function...Ch. 2.5 - Prob. 98ECh. 2.5 - Prob. 99ECh. 2.5 - Prob. 100ECh. 2.5 - Prob. 101ECh. 2.5 - Prob. 102ECh. 2.5 - Prob. 103ECh. 2.5 - Prob. 104ECh. 2.5 - Prob. 105ECh. 2.5 - Prob. 106ECh. 2.5 - Prob. 107ECh. 2.5 - Prob. 108ECh. 2.5 - Prob. 109ECh. 2.5 - Prob. 110ECh. 2.5 - Prob. 111ECh. 2.5 - Prob. 112ECh. 2.5 - Costly Computers A school district purchased x...Ch. 2.5 - Prob. 114ECh. 2.5 - Prob. 1PQCh. 2.5 - 2. If f = {(5, 4), (3, 6), (2, 5)}, then what is...Ch. 2.5 - Prob. 3PQCh. 2.5 - Prob. 4PQCh. 2.5 - Prob. 5PQCh. 2.5 - Prob. 6PQCh. 2.5 - Prob. 7PQCh. 2.5 - LINKING concepts... For Individual or Group...Ch. 2.6 - True or False? Explain. If the cost of an 800...Ch. 2.6 - True or False? Explain.
2. If bananas are $0.39...Ch. 2.6 - Prob. 3FTCh. 2.6 - Prob. 4FTCh. 2.6 - True or False? Explain. The number πp is a...Ch. 2.6 - Prob. 6FTCh. 2.6 - Prob. 7FTCh. 2.6 - Prob. 8FTCh. 2.6 - Prob. 9FTCh. 2.6 - Prob. 10FTCh. 2.6 - Prob. 1ECh. 2.6 - Fill in the blank.
2. If y = kx, then k is the...Ch. 2.6 - Prob. 3ECh. 2.6 - Prob. 4ECh. 2.6 - Construct a function that expresses the...Ch. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Construct a function that expresses the...Ch. 2.6 - Prob. 9ECh. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Construct a function that expresses the...Ch. 2.6 - For each formula that illustrates a type of...Ch. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Prob. 17ECh. 2.6 - Prob. 18ECh. 2.6 - Prob. 19ECh. 2.6 - For each formula that illustrates a type of...Ch. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Prob. 23ECh. 2.6 - Prob. 24ECh. 2.6 - Find the constant of variation and construct the...Ch. 2.6 - Prob. 26ECh. 2.6 - Find the constant of variation and construct the...Ch. 2.6 - Prob. 28ECh. 2.6 - Prob. 29ECh. 2.6 - Prob. 30ECh. 2.6 - Prob. 31ECh. 2.6 - Prob. 32ECh. 2.6 - Prob. 33ECh. 2.6 - Prob. 34ECh. 2.6 - Solve each variation problem.
35. If P is...Ch. 2.6 - Solve each variation problem.
36. If H varies...Ch. 2.6 - Solve each variation problem.
37. If A varies...Ch. 2.6 - Solve each variation problem.
38. If J is jointly...Ch. 2.6 - Solve each variation problem.
39. If y is directly...Ch. 2.6 - Solve each variation problem.
40. If q is directly...Ch. 2.6 - Determine whether the first variable varies...Ch. 2.6 - Prob. 42ECh. 2.6 - Prob. 43ECh. 2.6 - Prob. 44ECh. 2.6 - Prob. 45ECh. 2.6 - Prob. 46ECh. 2.6 - Prob. 47ECh. 2.6 - Prob. 48ECh. 2.6 - Prob. 49ECh. 2.6 - Prob. 50ECh. 2.6 - Prob. 51ECh. 2.6 - Prob. 52ECh. 2.6 - Solve each problem. First-Class Diver The pressure...Ch. 2.6 - Solve each problem. Second Place The elephant seal...Ch. 2.6 - Solve each problem. Processing Oysters The time...Ch. 2.6 - Solve each problem.
56. View from an Airplane The...Ch. 2.6 - Prob. 57ECh. 2.6 - Solve each problem. Free Fall at Six Flags...Ch. 2.6 - Solve each problem. Cost of Plastic Sewer Pipe The...Ch. 2.6 - Solve each problem.
60. Cost of Copper Tubing A...Ch. 2.6 - Prob. 61ECh. 2.6 - Solve each problem.
62. Nitrogen Gas Shock...Ch. 2.6 - Prob. 63ECh. 2.6 - Prob. 64ECh. 2.6 - Prob. 65ECh. 2.6 - Prob. 66ECh. 2.6 - Solve each problem. Grade on an Algebra Test...Ch. 2.6 - Solve each problem.
68. Carpeting a Room The cost...Ch. 2.6 - Prob. 69ECh. 2.6 - Prob. 71ECh. 2.6 - Prob. 72ECh. 2.6 - Prob. 73ECh. 2.6 - Prob. 74ECh. 2.6 - Prob. 75ECh. 2.6 - Prob. 76ECh. 2.6 - Prob. 77ECh. 2.6 - Prob. 78ECh. 2.6 - Prob. 79ECh. 2.6 - Prob. 80ECh. 2.6 - Prob. 1PQCh. 2.6 - Prob. 2PQCh. 2.6 - Prob. 3PQCh. 2.6 - Prob. 4PQCh. 2.6 - Prob. LCCh. 2 - Graph each set of ordered pairs. State the domain...Ch. 2 - Graph each set of ordered pairs. State the domain...Ch. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Graph each set of ordered pairs. State the domain...Ch. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Prob. 31RECh. 2 - Prob. 32RECh. 2 - Let f ( x ) = x 2 + 3 a n d g ( x ) = 2 x − 7....Ch. 2 - Prob. 34RECh. 2 - Prob. 35RECh. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - Prob. 40RECh. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Prob. 49RECh. 2 - Prob. 50RECh. 2 - Prob. 51RECh. 2 - Prob. 52RECh. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Prob. 55RECh. 2 - Prob. 56RECh. 2 - Prob. 57RECh. 2 - Prob. 58RECh. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 63RECh. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - Prob. 68RECh. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Prob. 73RECh. 2 - Prob. 74RECh. 2 - Prob. 75RECh. 2 - Prob. 76RECh. 2 - Prob. 77RECh. 2 - Prob. 78RECh. 2 - Prob. 79RECh. 2 - Prob. 80RECh. 2 - Prob. 81RECh. 2 - Prob. 82RECh. 2 - Prob. 83RECh. 2 - Prob. 84RECh. 2 - Prob. 85RECh. 2 - Prob. 86RECh. 2 - Prob. 87RECh. 2 - Prob. 88RECh. 2 - Prob. 89RECh. 2 - Prob. 90RECh. 2 - Prob. 91RECh. 2 - Prob. 92RECh. 2 - Prob. 93RECh. 2 - Prob. 94RECh. 2 - Prob. 95RECh. 2 - Prob. 96RECh. 2 - Prob. 97RECh. 2 - Prob. 98RECh. 2 - Prob. 99RECh. 2 - Prob. 100RECh. 2 - Prob. 101RECh. 2 - Prob. 102RECh. 2 - Prob. 103RECh. 2 - Prob. 104RECh. 2 - Prob. 105RECh. 2 - Prob. 106RECh. 2 - Prob. 107RECh. 2 - Prob. 108RECh. 2 - Prob. 109RECh. 2 - Prob. 110RECh. 2 - Prob. 111RECh. 2 - Prob. 112RECh. 2 - Prob. 113RECh. 2 - Prob. 114RECh. 2 - Prob. 115RECh. 2 - Prob. 116RECh. 2 - Prob. 117RECh. 2 - Prob. 118RECh. 2 - Prob. 119RECh. 2 - Prob. 120RECh. 2 - Prob. 121RECh. 2 - Prob. 122RECh. 2 - Prob. 123RECh. 2 - Prob. 124RECh. 2 - Prob. 125RECh. 2 - Prob. 126RECh. 2 - Prob. 127RECh. 2 - Prob. 128RECh. 2 - Prob. 129RECh. 2 - Prob. 130RECh. 2 - Area of a Polygon Find the exact area of the...Ch. 2 - Whole Lotta Shakin' At the start of an economic...Ch. 2 - Prob. 1CTCh. 2 - Prob. 2CTCh. 2 - Prob. 3CTCh. 2 - Determine whether each equation defines y as a...Ch. 2 - Prob. 5CTCh. 2 - Prob. 6CTCh. 2 - Prob. 7CTCh. 2 - Prob. 8CTCh. 2 - Prob. 9CTCh. 2 - Prob. 10CTCh. 2 - Prob. 11CTCh. 2 - Prob. 12CTCh. 2 - Prob. 13CTCh. 2 - Prob. 14CTCh. 2 - Prob. 15CTCh. 2 - Prob. 16CTCh. 2 - Prob. 17CTCh. 2 - Prob. 18CTCh. 2 - Prob. 19CTCh. 2 - Prob. 20CTCh. 2 - Prob. 21CTCh. 2 - Prob. 22CTCh. 2 - Prob. 23CTCh. 2 - Prob. 24CTCh. 2 - Prob. 25CTCh. 2 - Prob. 26CTCh. 2 - Prob. 27CTCh. 2 - Prob. 28CTCh. 2 - Solve each equation. 2 x − 3 = 0Ch. 2 - Prob. 2TATCh. 2 - Prob. 3TATCh. 2 - Prob. 4TATCh. 2 - Prob. 5TATCh. 2 - Prob. 6TATCh. 2 - Prob. 7TATCh. 2 - Prob. 8TATCh. 2 - Prob. 9TATCh. 2 - Prob. 10TATCh. 2 - Prob. 11TATCh. 2 - Prob. 12TATCh. 2 - Prob. 13TATCh. 2 - Prob. 14TATCh. 2 - Prob. 15TATCh. 2 - Prob. 16TATCh. 2 - Prob. 17TATCh. 2 - Prob. 18TATCh. 2 - Prob. 19TATCh. 2 - Prob. 20TATCh. 2 - Prob. 21TATCh. 2 - Prob. 22TATCh. 2 - Prob. 23TATCh. 2 - Prob. 24TATCh. 2 - Prob. 25TATCh. 2 - Prob. 26TATCh. 2 - Prob. 27TATCh. 2 - Prob. 28TATCh. 2 - Prob. 29TATCh. 2 - Prob. 30TATCh. 2 - Prob. 31TATCh. 2 - Prob. 32TATCh. 2 - Prob. 33TATCh. 2 - Prob. 34TATCh. 2 - Prob. 35TATCh. 2 - Prob. 36TATCh. 2 - Prob. 37TATCh. 2 - Prob. 38TATCh. 2 - Prob. 39TATCh. 2 - Prob. 40TATCh. 2 - Prob. 41TATCh. 2 - Prob. 42TATCh. 2 - Prob. 43TATCh. 2 - Prob. 44TATCh. 2 - Prob. 45TATCh. 2 - Prob. 46TATCh. 2 - Prob. 47TATCh. 2 - Prob. 48TATCh. 2 - Prob. 49TATCh. 2 - Prob. 50TAT
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