Algebra 1 Functions and Function Notation Worksheet (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

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Mapping diagram.

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

Exercise 4 – Table check

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A table of values.

Determine whether the table shows \(y\) as a function of \(x\).

Exercise 5 – Vertical line test

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A line.

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

Exercise 6 – Circle graph

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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

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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

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A line segment.

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

Exercise 16 – Gas cost

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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

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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.

See the solutions: Functions and Function Notation worksheet solutions

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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Algebra 1 Functions and Function Notation Worksheet

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