Practice Function in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A function is a rule that assigns to each input in the domain exactly one output in the codomain — every input maps to precisely one output, never two.

A machine: put something in, get exactly one thing out. Same input always gives same output.

Showing a random 20 of 50 problems.

Example 1

medium
For f(x)=∣x∣, find f(−7)+f(7).

Example 2

medium
Given f(x)=2x2−3x+1, find f(4) and determine if g={(1,2),(3,4),(1,5)} is a function.

Example 3

easy
Is the set {(0,1),(1,2),(2,3),(3,4)} a function?

Example 4

challenge
If f(x)=ax+bx and f(1)=4, f(2)=3, find a+b.

Example 5

challenge
How many functions f:{1,2,3,4}→{1,2,3,4} are one-to-one?

Example 6

easy
If f(x)=x2, find f(−3).

Example 7

easy
If f(x)=3x−5, find f(0).

Example 8

medium
If f(x)=x2−x, compute f(3)−f(2).

Example 9

medium
If f(x)=x−4, find f(13).

Example 10

hard
If f(x)=x2−4x+1, find f(x+2), simplified.

Example 11

hard
State the domain of f(x)=x+2x−3.

Example 12

easy
Does the rule 'add 3 to the input' define a function?

Example 13

medium
If f(x)=2x+3 and f(a)=11, find a.

Example 14

easy
If f(x)=1x, what is f(0)?

Example 15

easy
True or false: a function can have two different inputs that share the same output.

Example 16

medium
A function f satisfies f(x)=3x−2. For which input is f(x)=10?

Example 17

medium
A function satisfies f(2x)=4x+1. Find f(x).

Example 18

challenge
f is defined on integers by f(1)=1 and f(n)=f(n−1)+n. Find f(5).

Example 19

easy
Is the set {(1,2),(2,3),(3,4)} a function?

Example 20

easy
If g(x)=x2−1, find g(−2).
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