Use the image to answer the question.

Question

A coordinate plane labeled 'Horizontal Shift in the Demand Curve' has axes ranging from 0 to 50, both by 5-unit increments. The x-axis is labeled 'Number of Units' and the y-axis is labeled 'Price' with dollar units. Two line segments are plotted.

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

(1 point)
Responses

8
8

2
2

5
5

10

Answer 1

To determine the value of \( k \) that characterizes the horizontal shift in the demand curve, we analyze the distance between the two lines on the graph.

If the left line is represented by \( y = f(x) \) and the right line by \( y = f(x - k) \), the value of \( k \) represents how much the curve shifts to the right.

Counting the distance on the x-axis between the two curves, if the right line is shifted to the right by 8 units, then \( k = 8 \). If it is shifted by 2, then \( k = 2 \), and likewise for 5 and 10.

If the graph clearly indicates that the shift is 8 units, then:

The correct answer is 8.