Which of the following identifies the value of k that would correctly characterize the horizontal shift shown in the graph if the line to the left represents y=f(x)

Question

𝑦
=
𝑓
(
𝑥
)
and the line to the right represents y=f(x−k)
𝑦
=
𝑓
(
𝑥
−
𝑘
)
?

(1 point)
Responses

10
10

8
8

5
5

2

Answer 1

The value of \( k \) represents the horizontal shift of the graph of the function. When you see a transformation like \( y = f(x - k) \), it indicates a shift to the right by \( k \) units. Conversely, \( y = f(x + k) \) would indicate a shift to the left by \( k \) units.

To determine the correct value of \( k \) based on the given information, you would need to know the specifics of the horizontal shift in the graph. Without seeing the shift explicitly, I can't tell you which of the values \( 10, 8, 5, \) or \( 2 \) is correct.

Generally, if the graph has moved to the right, you would take \( k \) as positive. If it's moved to the left, you would take \( k \) as negative.

If you have the specifics of the shift (such as how far the graph of \( y = f(x) \) has moved to the right or left), please provide that, and I can help you determine the correct value for \( k \).