
Concept explainers
In Problems 37−60, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all the steps. Be sure to show at least three key points. Find the domain and the range of each function.
g(x) = 3√12x

The domain and range of the function g(x)=3√12x and graph the function g(x)=3√12x using techniques of shifting, compressing, stretching and/or reflecting.
Answer to Problem 42AYU
Solution:
The graph of g(x)=3√12x is:
The domain and range of the function g(x)=3√12x is (−∞,∞).
Explanation of Solution
Given Information:
The function is g(x)=3√12x
Explanation:
Step 1: The cube root function y=3√x
Step 2: Replace x by 12x in the function y=√x
g(x)=3√12x.
The graph of function y=f(hx) is obtained from the graph of y=f(x) by multiplying each x− coordinate of y=f(x) by 1h
Replacing x by 12x results in horizontal compression by 12 units
Therefore, multiply each x− coordinate of y=√x by 2.
Hence, the graph of g(x)=3√12x is as follows:
The domain and range of the function y=3√x is (−∞,∞)
Also, the domain and range of the function g(x)=3√12x is (−∞,∞)
Chapter 2 Solutions
Precalculus
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