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

10
10

8
8

2
2

5

Answer 1

To determine the value of k for the horizontal shift of the demand curve from \( y = f(x) \) to \( y = f(x - k) \), you need to analyze the horizontal movement of the lines on the graph.

1. Identify the position of the original demand curve \( y = f(x) \) (the left line).
2. Identify the position of the shifted demand curve \( y = f(x - k) \) (the right line).
3. Measure the horizontal distance between the two lines on the graph.

The value of k will be equal to the horizontal distance between the original line and the shifted line to the right. Based on the options provided (10, 8, 2, 5), you will need to determine which option corresponds to the measured distance.

Without the image to reference, I can suggest that if you are seeing a shift, you count the units on the x-axis between the two lines. Depending on where those lines are positioned, your answer will be the appropriate choice among the listed options.

For example, if the line representing \( y = f(x) \) is at 15 and the line representing \( y = f(x - k) \) is at 25, then \( k = 10 \). If you determine the distance to be 5 units, then \( k = 5\), and so forth.

Please check the shifts visually on the graph and select the corresponding value of k based on your observations.