Unit 6 · Functions & Function Notation
f(x) is not f times x. It names the output of function f at input x.
f(3) = 11 reads “f of 3 equals 11.” If f models height in inches after t years, f(3) = 11 means at 3 years the height is 11 inches.
A way to name a function and its output, written f(x).
Example: If f(x) = 2x + 1, then f(4) = 9.
Try the prompt first. The steps stay folded until you ask to see them.
Let f(x) = −4x + 6. Find f(−2) and solve f(x) = 0.
Watch for
Treating f(x) as multiplication
The parentheses here mean “evaluate at,” not “multiply.”
Fix: Say “f of x” every time you read it.
Submit each answer to check it. The key is not shown until you do.
When babysitting, Nicole charges an hourly rate and an additional charge for gas. She uses the function C(h) = 6h + 5 to determine how much to charge for babysitting. The constant term of this function represents
Given g(x) = x³ + 2x² − x, evaluate g(−3).
The rule for a function of x is: multiply the input value by 2, then subtract 6. The data set for the input values of the function, x, is {−1, 1, 3, 5}. Which value is one of the output values, y?
Rewrite f(x) = 2x + 1 as a machine: input → ×2 → +1 → output.
Given f(x) = x² − 5x, interpret f(a + 1) − f(a) as a one-step change.
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