Question

Use the image to answer the 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.
▼Click for Long Desc
The first line segment passes through the following data points: left parenthesis 5 comma 45 right parenthesis, left parenthesis 10 comma 40 right parenthesis, left parenthesis 15 comma 35 right parenthesis, left parenthesis 20 comma 30 right parenthesis, left parenthesis 25 comma 25 right parenthesis, left parenthesis 30 comma 20 right parenthesis, left parenthesis 35 comma 15 right parenthesis, and left parenthesis 40 comma 10 right parenthesis. Three arrows directed rightward from this line segment are drawn to represent the line segment being shifted toward the right passing through the following data points: left parenthesis 15 comma 45 right parenthesis, left parenthesis 20 comma 40 right parenthesis, left parenthesis 25 comma 35 right parenthesis, left parenthesis 30 comma 30 right parenthesis, left parenthesis 35 comma 25 right parenthesis, left parenthesis 40 comma 20 right parenthesis, left parenthesis 45 comma 15 right parenthesis, and left parenthesis 50 comma 10 right parenthesis.

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)

10

2

5

8

Answer 1

10

Each corresponding point on the right-hand curve has its x-coordinate 10 units larger than on the left (e.g., (5,45) → (15,45)), so the graph is shifted right by 10, i.e. y = f(x−10).