Question

juan recently entered into a contract for a cell phone plan. the table shows the monthly cost in dollars, f(x), if juan sends x text messages.
x | 0 | 1 | 2 | 3 | 4 | 5
f(x) | 10.00 | 10.02 | 10.04 | 10.06 | 10.08 | 10.10
what type of function is represented?

• linear
• quadratic
• logarithmic
• exponential

Explanation:

Step1: Check rate of change

Calculate the difference between consecutive $f(x)$ values:
$10.02 - 10.00 = 0.02$, $10.04 - 10.02 = 0.02$, $10.06 - 10.04 = 0.02$, $10.08 - 10.06 = 0.02$, $10.10 - 10.08 = 0.02$

Step2: Identify function type

The change in $f(x)$ is constant ($0.02$) for each 1-unit increase in $x$, which matches the definition of a linear function (constant slope/rate of change).

Answer:

linear