Algebra I

Functions: Evaluating

Lesson

A function is a rule that takes an input and produces an output. The notation $f(x)$ reads as “f of x.”

For example, if $f(x) = 2x + 3$ , then to find $f(5)$ , you substitute 5 for x and simplify:

f(5) = 2(5) + 3 = 10 + 3 = 13

The $f$ is the function’s name (it could be any letter — $g$ , $h$ , etc.). The $x$ in parentheses is the input variable. When you see $f(\text{number})$ , replace every $x$ in the rule with that number.

Worked example 1

Given $f(x) = 3x - 2$ , find $f(4)$ .

f(4) = 3(4) - 2 = 12 - 2 = 10

Worked example 2

Given $g(x) = x^2 + 1$ , find $g(-3)$ .

g(-3) = (-3)^2 + 1 = 9 + 1 = 10

Notice $(-3)^2 = 9$ (negative times negative is positive).

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

f(x) = x + 5; \text{ find } f(3)

Problem 2

f(x) = 2x; \text{ find } f(7)

Problem 3

f(x) = x - 2; \text{ find } f(10)

Problem 4

f(x) = 3x + 1; \text{ find } f(2)

Practice

Standard problems matching the lesson.

Problem 5

f(x) = 2x + 3; \text{ find } f(5)

Problem 6

f(x) = 3x - 2; \text{ find } f(4)

Problem 7

f(x) = 4x + 1; \text{ find } f(0)

Problem 8

f(x) = -2x + 7; \text{ find } f(3)

Problem 9

f(x) = 5x - 8; \text{ find } f(2)

Problem 10

g(x) = x^2 + 1; \text{ find } g(3)

Problem 11

g(x) = x^2 - 5; \text{ find } g(4)

Problem 12

f(x) = 2x + 3; \text{ find } f(-1)

Problem 13

f(x) = 3x - 4; \text{ find } f(-2)

Problem 14

h(x) = -x + 6; \text{ find } h(8)

Problem 15

f(x) = x^2; \text{ find } f(-5)

Problem 16

f(x) = 2x^2 - 3; \text{ find } f(2)

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 17

g(x) = x^2 + 1; \text{ find } g(-3)

Problem 18

f(x) = 3x^2 - 2x + 1; \text{ find } f(2)

Problem 19

f(x) = 2x^2 + x - 5; \text{ find } f(-1)

Problem 20

h(x) = -x^2 + 4x; \text{ find } h(3)

Problem 21

f(x) = x^3 - x; \text{ find } f(-2)

Problem 22

f(x) = \frac{x + 6}{2}; \text{ find } f(8)