Question

describe the transformations in $g(x) = 2|x - 1| + 5$ as it relates to the graph of the parent function
the graph of $g(x) = 2|x - 1| + 5$ is the graph of the parent function $\boldsymbol{\text{select choice}}$ and translated 5 units $\boldsymbol{\text{select choice}}$ and 1 unit $\boldsymbol{\text{select choice}}$

Explanation:

The parent function of \(g(x)=2|x-1|+5\) is \(f(x)=|x|\).

1. The coefficient \(2\) outside the absolute value represents a vertical stretch by a factor of 2.
2. The \(-1\) inside the absolute value (\(x-1\)) shifts the graph 1 unit to the right.
3. The \(+5\) outside the absolute value shifts the graph 5 units up.

Answer:

The graph of \(g(x) = 2|x - 1| + 5\) is the graph of the parent function vertically stretched by a factor of 2 and translated 5 units up and 1 unit right.