8:47 5G. 80% MATH 122 WORKSHEET 2 JANUARY 27, 2025 Solve the following problems on a separate sheet. Justify your answers to earn full credit. 1. Let F(x) = x²- 2 | x+1. (a) Write a piecewise formula for F which does not involve absolute values. (b) Plot a careful graph of y = F(x) and then state its domain and range. 2. A portion of the graph of the function y= f(x) is shown in the figure. (a) State the domain and range of f. (b) Find the values: f(-2) and f(3). (c) Use the graph to determine each of the limits: (i) lim f(x); lim f(x); lim f(x) x-2+ x-2- x-2 (ii) lim f(x); lim f(x); lim f(x). x-3+ x-3- x-3 3. The graph of the function y = k(x) is shown in the figure. (a) Write a piecewise formula for the function. (b) Evaluate the one-sided limits of k at x=1 algebraically, by using your formula from part (a). 2 y=√(x) 2 1.5 y=k(x) 1 0 1 4. Let f(x) = |x| and g(x) = x − 3 . (a) Determine the formulas for each of the related composite functions: h(x)=(fog)(x) = f(g(x)) s(x) = (gf)(x) = g(f(x)) t(x) = (g • ƒ • g)(x) = g( ƒ (g(x))) . (b) Plot graphs of all the functions: f,h,s, and t in the same coordinate plane. Use different colors for distinction. 5. (a) Find the values of x₁ and x2 in the figure. (b) Find the largest positive number 6 such that: |1|<0.1 whenever 0 < | x-1 |< 8. =1+0.1- 1 - y = Hint: Choose > to be the minimum value of | x - 1 | for i = 1,2. 9 1-0.1- 10 I x₁ 1 x2 าน
8:47 5G. 80% MATH 122 WORKSHEET 2 JANUARY 27, 2025 Solve the following problems on a separate sheet. Justify your answers to earn full credit. 1. Let F(x) = x²- 2 | x+1. (a) Write a piecewise formula for F which does not involve absolute values. (b) Plot a careful graph of y = F(x) and then state its domain and range. 2. A portion of the graph of the function y= f(x) is shown in the figure. (a) State the domain and range of f. (b) Find the values: f(-2) and f(3). (c) Use the graph to determine each of the limits: (i) lim f(x); lim f(x); lim f(x) x-2+ x-2- x-2 (ii) lim f(x); lim f(x); lim f(x). x-3+ x-3- x-3 3. The graph of the function y = k(x) is shown in the figure. (a) Write a piecewise formula for the function. (b) Evaluate the one-sided limits of k at x=1 algebraically, by using your formula from part (a). 2 y=√(x) 2 1.5 y=k(x) 1 0 1 4. Let f(x) = |x| and g(x) = x − 3 . (a) Determine the formulas for each of the related composite functions: h(x)=(fog)(x) = f(g(x)) s(x) = (gf)(x) = g(f(x)) t(x) = (g • ƒ • g)(x) = g( ƒ (g(x))) . (b) Plot graphs of all the functions: f,h,s, and t in the same coordinate plane. Use different colors for distinction. 5. (a) Find the values of x₁ and x2 in the figure. (b) Find the largest positive number 6 such that: |1|<0.1 whenever 0 < | x-1 |< 8. =1+0.1- 1 - y = Hint: Choose > to be the minimum value of | x - 1 | for i = 1,2. 9 1-0.1- 10 I x₁ 1 x2 าน
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 35E
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Question 3 and 4
Transcribed Image Text:8:47
5G. 80%
MATH 122
WORKSHEET 2
JANUARY 27, 2025
Solve the following problems on a separate sheet. Justify your answers to earn full credit.
1. Let F(x) = x²- 2 | x+1.
(a) Write a piecewise formula for F which does not involve absolute values.
(b) Plot a careful graph of y = F(x) and then state its domain and range.
2. A portion of the graph of the function
y= f(x) is shown in the figure.
(a) State the domain and range of f.
(b) Find the values: f(-2) and f(3).
(c) Use the graph to determine each of
the limits:
(i)
lim f(x);
lim f(x);
lim f(x)
x-2+
x-2-
x-2
(ii) lim f(x);
lim f(x);
lim f(x).
x-3+
x-3-
x-3
3. The graph of the function y = k(x) is
shown in the figure.
(a) Write a piecewise formula for the
function.
(b) Evaluate the one-sided limits of
k at x=1 algebraically, by using
your formula from part (a).
2
y=√(x)
2
1.5
y=k(x)
1
0
1
4. Let f(x) = |x| and g(x) = x − 3 .
(a) Determine the formulas for each of the related composite functions:
h(x)=(fog)(x) = f(g(x))
s(x) = (gf)(x) = g(f(x))
t(x) = (g • ƒ • g)(x) = g( ƒ (g(x))) .
(b) Plot graphs of all the functions: f,h,s, and t in the same coordinate plane.
Use different colors for distinction.
5. (a) Find the values of x₁ and x2 in the figure.
(b) Find the largest positive number 6 such that:
|1|<0.1 whenever 0 < | x-1 |< 8.
=1+0.1-
1 -
y =
Hint:
Choose > to be the minimum value of | x - 1 | for i = 1,2.
9
1-0.1-
10
I
x₁ 1
x2
าน
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