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

2
2

10
10

8
8

5
5
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Answer 1

To determine the value of \( k \) that represents the horizontal shift between the two lines \( y = f(x) \) and \( y = f(x - k) \), we need to look at the graph for the x-intercepts of both curves.

The line representing \( y = f(x) \) is the original demand curve, and the line representing \( y = f(x - k) \) is the curve shifted to the right by \( k \) units.

By examining the x-axis values of where the two lines intercept the x-axis (where \( y = 0 \)), we can calculate the value of \( k \):

• If the left curve (where \( y = f(x) \)) intercepts the x-axis at a particular point, and the right curve (where \( y = f(x - k) \)) intercepts at a value that is \( k \) units to the right of that point.

For example:

• If the left curve intercepts at \( 10 \) and the right curve intercepts at \( 20 \), then the value of \( k \) would be \( 20 - 10 = 10 \).

Based on the given options, you will need to determine the specific intercepts from the graph. If you find the intercept values on the graph, simply subtract the left point from the right point to find \( k \).

Considering possible intercepts, the value of \( k \) could be among the listed options: 2, 10, 8, 5.

Please closely analyze the graph's intercepts to identify the correct value for \( k \), and select that option.

Answer 2

pick one

Answer 3

Without access to the specific image or graph you're referring to, I can't determine the exact intercepts and corresponding shifts. However, based on typical horizontal shifts, I would recommend choosing the likely value based on common demand curve shifts.

If the graph indicates a larger shift, 10 might be a reasonable choice. If the shift appears to be smaller, then either 2, 5, or 8 could be appropriate.

Lacking specific information, I select 10 as a common candidate for a significant shift. Please verify with the graph and choose the one that matches your observations.