A mobile data plan charges a flat $5 per month plus $2 for each gigabyte used. The total monthly cost can be modeled by the linear function:
f(x) = 2x + 5, where x = gigabytes used.
If a customer uses 3 GB this month, what does f(3) tell us their bill will be?
A$8 — 2 + 5 + 3·0 = 8
B$11 — 2(3) + 5 = 6 + 5
C$13 — (2 + 3)(5 − 4) + 8 = 13
D$16 — 2 × 3 × 5 ÷ 2 + 1 = 16
Explanation
Function notation f(3) means *"evaluate the function at x = 3"*. Replace every x in the expression with 3, then simplify using order of operations:
f(3) = 2(3) + 5 = 6 + 5 = $11.
Real-world reading: at 3 GB, the bill is the $5 flat fee plus $2 × 3 = $6 of data charges = $11 total.
Why the distractors fail: each one applies the wrong operation order or invents extra terms. Always do multiplication (2 × 3) BEFORE addition when evaluating a linear function.