Question

The piecewise function h(x) is shown on the graph.

On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (negative 4, negative 4) and goes up to an open circle at (negative 1, 2). The second line has a closed circle at (negative 1, 3), continues horizontally to (1, 3), and then goes down to a closed circle at (4, 0).
What is the value of h(3)?

–2
–1
1
2

Answer 1

Explanation:

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.