Algebra 1 Functions and Function Notation Worksheet (PDF)

Algebra 1 math worksheet: Functions and Function Notation – Maths PDF

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This algebra 1 functions worksheet for Algebra 1 covers functions and function notation (Common Core F-IF.A.1, F-IF.A.2, F-IF.B.5), with a free PDF to print.

This worksheet has 20 problems on functions and function notation, aligned to Common Core F-IF.A.1, F-IF.A.2, and F-IF.B.5. You will test relations with the vertical line test, evaluate f(x), find domain and range, and use functions to model prices and heights. Early problems check one skill at a time; the final six put the skill inside real situations. Write each step on paper before you look at the answer key.

Algebra 1 · Common Core State Standards: F-IF.A.1, F-IF.A.2, F-IF.B.5

Algebra 1 functions worksheet: exercises 1 to 10

Exercise 1 – Function or not

Determine whether the relation $\{(1, 2), (2, 4), (3, 6), (4, 8)\}$ is a function.

Exercise 2 – Repeated input

Determine whether the relation $\{(1, 5), (2, 7), (1, 9)\}$ is a function.

Exercise 3 – Mapping diagram

Mapping diagram.

Determine whether the mapping represents a function. Then give the domain and range.

Exercise 4 – Table check

A table of values.

Determine whether the table shows $y$ as a function of $x$.

Exercise 5 – Vertical line test

A line.

Use the vertical line test to decide whether the graph is a function.

Exercise 6 – Circle graph

A circle.

Use the vertical line test to decide whether the graph of a circle is a function.

Exercise 7 – Evaluate a function

For $f(x) = 3x – 4$, find $f(5)$.

Exercise 8 – Quadratic function value

For $f(x) = x^{2} + 2x – 3$, find $f(-3)$.

Exercise 9 – Negative input

For $g(x) = -2x + 7$, find $g(-4)$.

Exercise 10 – Evaluate h

For $h(t) = 5t^{2} – 3$, find $h(2)$.

Exercises 11 and up

Exercise 11 – Find the input

For $f(x) = 2x + 1$, find $x$ when $f(x) = 15$.

Exercise 12 – Two functions

Let $f(x) = 2x – 1$ and $g(x) = x^{2}$. Find $f(3) + g(-2)$.

Exercise 13 – Read a table

Values of the function f.

The table lists values of a function $f$. Find $f(3)$ and write the value of $x$ for which $f(x) = 9$.

Exercise 14 – Domain and range

Give the domain and range of $\{(-2, 4), (0, 1), (3, 4), (5, -2)\}$.

Exercise 15 – Domain and range from a graph

A line segment.

The graph is a segment from $(-3, 1)$ to $(4, 5)$. Give the domain and range.

Exercise 16 – Gas cost

Cost in dollars for 0, 5, 10, and 15 gallons.

The cost of gasoline is $C(g) = 3.25g$ dollars for $g$ gallons. Find $C(12)$. The tank holds 15 gallons, so give the domain and range for this situation.

Exercise 17 – Concert fee

A ticket site charges $T(n) = 8n + 5$ dollars for $n$ tickets, including a $5 booking fee. Find $T(6)$, then find the number of tickets when $T(n) = 93$.

Exercise 18 – Rule in words

A function multiplies the input by 3 and then subtracts 2. Write the rule using function notation, find the output for the input $-4$, and find the input that gives the output 25.

Exercise 19 – Ball height

Height in feet after t seconds.

A ball’s height in feet after $t$ seconds is $h(t) = -16t^{2} + 48t$. Find $h(1)$, $h(2)$, and $h(3)$. Is the time a function of the height? Explain.

Exercise 20 – Taxi fare

A taxi fare is $F(m) = 2.50 + 1.75m$ dollars for $m$ miles. Find $F(8)$. Maya has $20. Find the greatest whole number of miles she can ride.

Exercise 21 – Explain functions

(a) Input: a student’s name; output: the student’s birth date. (b) Input: a birth date; output: the students in a school born on that date. Decide whether each situation is a function.

Key facts behind this algebra 1 functions worksheet

Key facts

A function assigns exactly one output to each input.
The domain is the set of inputs; the range is the set of outputs.
The vertical line test: a graph is a function if no vertical line meets it twice.
f(x) is read “f of x” and means the output when the input is x.
In context, the domain is limited to the inputs that make sense.

How to use this algebra 1 functions worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the algebra 1 functions worksheet as a PDF with the button below and keep it with your notes.

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