Question

which statement correctly describes the relationship between the graph of $f(x)$ and $g(x)=f(x - 7)$?

• the graph of $g(x)$ is the graph of $f(x)$ translated 7 units down.
• the graph of $g(x)$ is the graph of $f(x)$ translated 7 units left.
• the graph of $g(x)$ is the graph of $f(x)$ translated 7 units right.
• the graph of $g(x)$ is the graph of $f(x)$ translated 7 units up.

Explanation:

For function transformations, when $g(x) = f(x - h)$ where $h>0$, the graph of $f(x)$ shifts $h$ units to the right.[LLM SSE On Failure]

Answer:

The graph of $g(x)$ is the graph of $f(x)$ translated 7 units right.