Question

which statement correctly describes the relationship between the graph of $f(x)$ and the graph of $g(x)=f(x)-4$?

• the graph of $g(x)$ is the graph of $f(x)$ translated 4 units down.
• the graph of $g(x)$ is the graph of $f(x)$ translated 4 units up.
• the graph of $g(x)$ is the graph of $f(x)$ translated 4 units left.
• the graph of $g(x)$ is the graph of $f(x)$ translated 4 units right.

Explanation:

For function transformations, when you have $g(x) = f(x) - k$ where $k>0$, this represents a vertical translation of the graph of $f(x)$ downward by $k$ units. Here, $k=4$, so the graph of $g(x)$ is $f(x)$ shifted 4 units down.

Answer:

The graph of $g(x)$ is the graph of $f(x)$ translated 4 units down.