(a)
To identify: the parent function f(x) of g(x)
(a)

Explanation of Solution
Given information:
Consider g(x)=|x−1|+2
Parent function is the simplest function of family of functions, which has the same shape as that of entire family.
We have g(x)=|x−1|+2
The function f(x)=|x| is the simplest function and have same shape as that of
g(x).
Hence, the parent function is f(x)=|x| .
(b)
To explain: the sequence of transformations from f(x) to g(x).
(b)

Explanation of Solution
Given information:
Consider g(x)=|x−1|+2
The parent function is f(x)=|x| .
If The function f(x)=|x| is right shift one unit and vertical up shift two units, then
g(x)=|x−1|+2 is obtained.
Hence, the transformation of f to g is “ right shift 1 unit up shift 2 units”.
(c)
To sketch: the graph of g(x)
(c)

Explanation of Solution
Given information:
Consider g(x)=|x−1|+2
Graph:
The graph of g(x)=|x−1|+2
(d)
To write: the function g(x) in terms of f(x)
(d)

Explanation of Solution
Given information:
Consider g(x)=|x−1|+2
Parent function is f(x)=|x|
We have
g(x)=|x−1|+2=f(x−1)+2
Hence, the parent function is g(x)=f(x−1)+2 .
Chapter 1 Solutions
EBK PRECALCULUS W/LIMITS
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