Question

The graph represents the data cost for monthly Internet service for a cell phone.

On a coordinate plane, a graph titled Cell Phone Internet Service shows Gigabytes Used on the x-axis and Monthly Cost in dollars on the y-axis. A piecewise function has 3 lines. The 1st line has a closed circle at (0, 15), continues horizontally at y = 15, then has a closed circle at (2, 15). The 2nd line has an open circle at (2, 20) and then continues up to a closed circle at (6, 40). The 3rd line has an open circle at (6, 50) and then continues horizontally at y = 50.
Which function, C(x), represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month?

Answer 1

A

Explanation:

Answer 2

C(x) = 15 0 ≤ x ≤ 2

C(x) = 5x + 10 2 < x ≤ 6

C(x) = 50 x > 6

Explanation:

Let's define

• x: Gigabytes Used

• C(x): Monthly Cost in dollars

The graph has three parts. In the first part, the cost has a constant value of 15. The closed circles indicate that endpoints (at 0 and 2) are included in this segment.

In the second part, a line (which pass through (2, 20) and (6,40)) is shown. Its parameters are:

slope = (40 - 20)/(6-2) = 5

y-intercept: 20 = 5*2 + b <=> b = 20 - 5*2 = 10

Therefore, the equation of the line is: y = 5x + 10

The open circle at the beginning of the line indicates that it is not present in the segment. The closed circle at the end of the line indicates that it is present in the segment.

In the third part, the cost has a constant value of 50. The open circle indicates that the endpoint (6,50) is not included in this segment.