Introduction to Functions

Understand what functions are and how to represent them

Written and reviewed by the Study Mondo Education TeamLast updated February 16, 2026

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Introduction to Functions

What is a Function?

A function is a relationship where each input has exactly one output.

Example: $y = 2x + 3$

For each value of $x$ , there's exactly one value of $y$ .

Function Notation

$f(x) = 2x + 3$

Read as: "f of x equals 2x plus 3"

Example: Find $f(4)$ $f(4) = 2(4) + 3 = 11$

Four Ways to Represent Functions

1. Equation

$f(x) = 2x + 1$

2. Table

x	y
0	1
1	3
2	5

3. Graph

A line or curve on a coordinate plane

4. Words

"The output is one more than twice the input"

Is It a Function?

Vertical Line Test: If a vertical line touches the graph at more than one point, it's NOT a function.

📚 Practice Problems

1Problem 1easy

❓ Question:

If $f(x) = 3x - 2$ , find $f(5)$ .

💡 Show Solution

Solution:

Substitute $x = 5$ into the function: $f(5) = 3(5) - 2$ $f(5) = 15 - 2$ $f(5) = 13$

Answer: $f(5) = 13$

2Problem 2easy

❓ Question:

If $f(x) = 3x - 2$ , find $f(5)$ .

💡 Show Solution

Solution:

Substitute $x = 5$ into the function: $f(5) = 3(5) - 2$ $f(5) = 15 - 2$ $f(5) = 13$

Answer: $f(5) = 13$

3Problem 3medium

❓ Question:

If $g(x) = x^2 + 4$ , find $g(-3)$ .

💡 Show Solution

Solution:

Substitute $x = -3$ : $g(-3) = (-3)^2 + 4$ $g(-3) = 9 + 4$ $g(-3) = 13$

Answer: $g(-3) = 13$

4Problem 4medium

❓ Question:

If $g(x) = x^2 + 4$ , find $g(-3)$ .

💡 Show Solution

Solution:

Substitute $x = -3$ : $g(-3) = (-3)^2 + 4$ $g(-3) = 9 + 4$ $g(-3) = 13$

Answer: $g(-3) = 13$

5Problem 5hard

❓ Question:

A function is defined by $h(x) = 2x + 5$ . For what value of $x$ is $h(x) = 17$ ?

💡 Show Solution

Solution:

Set the function equal to 17: $2x + 5 = 17$

Solve: $2x = 12$ $x = 6$

Check: $h(6) = 2(6) + 5 = 17$ ✓

Answer: $x = 6$

6Problem 6hard

❓ Question:

A function is defined by $h(x) = 2x + 5$ . For what value of $x$ is $h(x) = 17$ ?

💡 Show Solution

Solution:

Set the function equal to 17: $2x + 5 = 17$

Solve: $2x = 12$ $x = 6$

Check: $h(6) = 2(6) + 5 = 17$ ✓

Answer: $x = 6$

Explain using:

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Slope and Rate of Change

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❓ Frequently Asked Questions

What is Introduction to Functions?▾

Understand what functions are and how to represent them

How can I study Introduction to Functions effectively?▾

Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 6 problems provided, checking solutions as you go. Regular review and active practice are key to retention.

Is this Introduction to Functions study guide free?▾

Yes — all study notes, flashcards, and practice problems for Introduction to Functions on Study Mondo are free to access. No account is needed.

What course covers Introduction to Functions?▾

Introduction to Functions is part of the Grade 8 Math course on Study Mondo, specifically in the Linear Equations and Functions section. You can explore the full course for more related topics and practice resources.

Are there practice problems for Introduction to Functions?▾

Yes, this page includes 6 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.

Introduction to Functions

Try the Interactive Version!

Introduction to Functions

What is a Function?

Function Notation

Four Ways to Represent Functions

1. Equation

2. Table

3. Graph

4. Words

Is It a Function?

📚 Practice Problems

1Problem 1easy

❓ Question:

2Problem 2easy

❓ Question:

3Problem 3medium

❓ Question:

4Problem 4medium

❓ Question:

5Problem 5hard

❓ Question:

6Problem 6hard

❓ Question:

Practice Lab

Practice with Flashcards

Browse All Topics

📌 Related Topics in Linear Equations and Functions

❓ Frequently Asked Questions