If the parent function f(x) = |x| is transformed to g(x) = |x + 5|, what transformation occurs from f(x) to g(x)?

Question

The graph of f(x) is shifted upward to create g(x).
The graph of f(x) is shifted downward to create g(x).
The graph of f(x) is shifted to the right to create g(x).
The graph of f(x) is shifted to the left to create g(x).

Answer 1

To determine the transformation that occurs from the parent function \( f(x) = |x| \) to \( g(x) = |x + 5| \), we can analyze the expression inside the absolute value.

In \( g(x) = |x + 5| \), the term \( +5 \) indicates that we are shifting the graph of \( f(x) \) horizontally. Specifically, adding a positive value inside the absolute value function leads to a shift to the left.

Thus, the transformation from \( f(x) \) to \( g(x) \) is:

The graph of \( f(x) \) is shifted to the left to create \( g(x) \).