In Exercises 1-5, graph f and g in the same rectangular
f(x)=2x and g(x)=2x−3
To calculate: Domain, range and equation of asymptotes for given functions f(x)=2x,g(x)=2x−3.
Answer to Problem 1MCCP
Solution:
Asymptote of f:y=3_.
Asymptote of g:y=−3_.
Domain of f = Domain of g=(−∞,∞).
Range of f=(0,∞)_, Range of g=(−3,∞)_.
Explanation of Solution
Given: The given functions: f(x)=2x,g(x)=2x−3
Calculation:
Create a table of co-ordinates for the given function f(x)=2x
x |
-2 |
-1 |
0 |
1 |
2 |
f(x)=2x |
f(−2)=2−2=122=14 |
f(−1)=2−1=121=12 |
f(0)=20=1 |
f(1)=21=2 |
f(2)=22=4 |
Plot these points, connecting them with a curve for graph of f(x)=2x.
To plot the graph of a given function g(x)=bx−c=2x−3, shift the graph of f(x)=bx=2x downwards c=3 units.
To graph: f(x)=2x,g(x)=2x−3
Explanation of Solution
Given: The given functions: f(x)=2x,g(x)=2x−3
Graph:
Interpretation:
The graph for f(x)=2x never touches negative portion of x-axis. Hence x-axis or y=0 is asymptote.
The asymptote for g(x)=2x−3 is y=−3.
Domain of f(x)=bx and g(x)=bx−c consists of all real numbers (−∞,∞).
Hence domain of f(x)=2x= domain of g(x)=2x−3 =(−∞,∞).
Range of f(x)=bx consists of all positive real numbers (0,∞).
Hence range of f(x)=2x is (0,∞).
From the graph, range of g(x)=2x−3 is (−3,∞).
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Chapter 4 Solutions
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