QuestionHow does the graph of $g(x)=f(x-5)$ compare to $f(x)$ ? A. up 5 B. down 5 C. left 5 D. right 5

Studdy Solution

STEP 1

Assumptions1. $g(x)=f(x-5)$ . We have four possible transformations of the graph of $f(x)$ to obtain the graph of $g(x)$ shifting5 units up, down, to the left, or to the right.

STEP 2

We need to understand the effect of the transformation $f(x-5)$ on the graph of $f(x)$ . In general, if we have a function $f(x)$ and we replace $x$ with $(x-h)$ , the graph of the new function, $f(x-h)$ , will be a horizontal shift of the graph of $f(x)$ .

STEP 3

The direction of the shift depends on the sign of $h$ . If $h$ is positive, the graph shifts to the right by $h$ units. If $h$ is negative, the graph shifts to the left by $-h$ units.

STEP 4

In our case, $h=$ in the function $g(x)=f(x-)$ . Therefore, the graph of $g(x)$ is a shift of the graph of $f(x)$ to the right by units.
The correct answer is D. The graph of $g(x)$ is the graph of $f(x)$ shifted units to the right.

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