Practice Function as Mapping in Math

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

Viewing a function as a mapping means thinking of it as an explicit association from each element of the domain to exactly one element of the codomain.

Like a dictionary: every word maps to a definition. Every input maps to an output.

Showing a random 20 of 50 problems.

Example 1

easy
In the dictionary mapping word→definition, what plays the role of input?

Example 2

medium
A mapping diagram has an input arrow from 4 with no arrow leaving it. Is it a function on its stated domain?

Example 3

easy
Is the set of pairs {(5,8),(6,8),(7,8)} a function?

Example 4

medium
Restricting f(x)=x2 to x≥0 makes it one-to-one. What does that mean for the mapping?

Example 5

easy
Which of the following sets of ordered pairs defines a function from {1,2,3} to R? (A) {(1,5),(2,5),(3,5)} (B) {(1,2),(2,3)} (C) {(1,0),(2,1),(3,2),(1,4)}

Example 6

medium
Explain why the relation R={(1,2),(1,3),(2,5)} is NOT a function from {1,2} to {2,3,5}.

Example 7

medium
Let f:R→R, f(x)=x2. Find f−1({4}) (the pre-image of 4) and explain why f does not have an inverse function on all of R.

Example 8

easy
Is {(1,1),(2,4),(3,9),(4,16)} a function?

Example 9

easy
Is the set of pairs {(1,2),(2,4),(3,6)} a function?

Example 10

medium
A vending machine maps each button to one snack, but two buttons give chips. Function?

Example 11

medium
Domain {a,b}, codomain {1,2}. How many distinct functions exist?

Example 12

easy
Let f:{1,2,3}→{a,b,c} be defined by f(1)=a, f(2)=a, f(3)=c. Determine whether f is a valid function, and find its range.

Example 13

medium
Let f:{1,2,3,4}→{a,b,c} with f(1)=a, f(2)=b, f(3)=a, f(4)=c. Find the range and decide if f is one-to-one.

Example 14

hard
Domain {1,2,3,4}, codomain {a,b}. How many functions are onto?

Example 15

easy
Does a vertical line graph represent a function?

Example 16

challenge
Domain {a,b,c}, codomain {1,2}. How many functions are there, and how many are one-to-one?

Example 17

medium
A mapping f:{1,2,3,4,5}→{0,1} sends n to n mod 2. List the pre-image of 1.

Example 18

hard
Define f:R→R, f(x)=x3. Determine whether f is one-to-one and whether it is onto.

Example 19

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

Example 20

easy
Use the vertical line test: a graph hit twice by some vertical line. Function?
← Back to Function as Mapping Worked Examples Formula Explained