Use function notation; evaluate, interpret, and compare function values. | Functions | ACT Mathematics

Function notation names outputs, and differences compare two outputs.

Core Idea

Function notation is just a compact way to name outputs. $𝑓 (6)$ means the output when the input is 6, and expressions such as $𝑓 (6) - 𝑓 (2)$ compare outputs at two inputs.

Understanding

Rule: Many ACT function-notation questions are easier when you translate them into words before you calculate. For example, $𝐶 (6) - 𝐶 (2)$ means the difference between the cost at 6 hours and the cost at 2 hours. That is a comparison, not a single function value.

This matters because students often evaluate one part correctly and then misread what the whole expression means. Keep track of whether the question asks for one output, a difference of outputs, or a statement about what those values mean in context.

Misconceptions

Treating $𝑓 (6) - 𝑓 (2)$ as the same thing as $𝑓 (4)$ .
Reading the input value as multiplication.
Finding a correct numerical value but attaching the wrong meaning to it.

Question

Worked Example

A parking garage charges according to $𝐶 (ℎ) = 4 + 2.5 ℎ$ , where $ℎ$ is the number of hours parked. What does $𝐶 (6) - 𝐶 (2)$ represent?

Select an answer to see the explanation