Question

select the correct option from each drop - down to complete the sentences.
if the function $f(x)$ is replaced by $f(x - 3)$, then the graph will shift 3 units
if the function $f(x)$ is replaced by $f(x + 2)$, then the graph will shift 2 units
options for shift direction: horizontally, to the left; horizontally, to the right

Explanation:

Step1: Recall horizontal shift rules

For a function \( f(x) \), the transformation \( f(x - h) \) shifts the graph \( h \) units horizontally. If \( h>0 \), it shifts to the right; if \( h<0 \), it shifts to the left.

Step2: Analyze \( f(x - 3) \)

Here, \( h = 3>0 \), so the graph of \( f(x) \) replaced by \( f(x - 3) \) shifts 3 units horizontally, to the right.

Step3: Analyze \( f(x + 2) \)

Rewrite \( f(x + 2) \) as \( f(x - (-2)) \). Here, \( h=-2 \), so it shifts 2 units horizontally, to the left (since \( h=-2<0 \), equivalent to shifting left by 2 units).

Answer:

First drop - down: horizontally, to the right
Second drop - down: horizontally, to the left