Algebra and Graphs

Basic Expressions and Formulas

Introduction to Mappings

Introduction to Formulas

Expressions with One Variable

Equations and Simplifications

Simplifying Expressions

How to Solve an Equation

Solving Rational Equations

Simplifying Expressions with Multiple Variables

Expanding and Binomials

Expanding Double Brackets

Square of a Binomial

Quadratic Equations

Simple Quadratic Equations

Vertex Form and Parabola Transformations

Converting Quadratics: General and Vertex Form

Determining Quadratic Equations

Solving Simple Quadratic Equations

Factorization Method for Solving Quadratic Equations

Solving Quadratic Equations: Quadratic Formula

Functions and Graphs

Plotting and Reflecting Points on the Coordinate Grid

Introduction to Functions and Graphs

Gradient and Y-Intercept in Linear Equations

Finding the Equation of a Straight Line

1 of 2

Previous Lesson

{results_count} Math videos for {phrase}

Displaying {results_count} results of {results_count_total}

Generic filters

Exact matches only

Search in title

Search in content

Search in excerpt

Filter by Lesson Categories

Introduction to Functions and Graphs

Algebra and Graphs Introduction to Functions and Graphs

🎬 Video Tutorial

(0:01) What is a Function?: A function maps each input to exactly one output, often written as $f(x) = \text{expression}$ (e.g., $f(x) = 2x + 1$).
(1:14) Function Table and Graph: Create a table of input-output pairs (e.g., $f(1) = 3$, $f(2) = 5$) to visualise the function on a graph, making it easier to interpret.
(1:31) Unique Outputs for Each Input: A function cannot have the same x-value paired with different y-values.
(2:17) Finding Function Values from Graphs: To find $f(a)$, locate $x = a$ on the graph and read the corresponding y-value.

Membership Required

You must be a member of Math Angel Plus or Math Angel Unlimited to view this content.

Already a member? Log in here

📂 Revision Cards

Diagram explaining that a function transforms an "input" to one "output." — 1) Function

Visual representation of function notation showing the function f(x) = 2x + 1 and its calculated outputs for f(1), f(2), and f(3). — 2) Function Notation

Steps to graph a function showing a table of values for f(x)=2x+1 and its corresponding plotted graph with points. — 3) Plot a Graph

2 graphs showing non-functions: one with a circle and another with a vertical line, explaining that one x-value must not have multiple y-values. — 4) Graphs that do not represent a function

Graph showing function values with examples: f(-2) = -3 and f(x) = 0 at x = -4, 0, 5, with a function definition. — 5) Reading Function Values from Graphs

🍪 Quiz

0%

Introduction to Functions and Graphs

1 / 6

Q: What is the output of the function $f(x) = 3x + 2$ when $x = 5$?

15

23

20

17

Feedback: Not quite! When $x = 5$, $f(5) = 3(5) + 2 = 3 \times 5 + 2 = 17$

Feedback: Well done! When $x = 5$, $f(5) = 3(5) + 2 = 3 \times 5 + 2 = 17$

2 / 6

Q: What is the output of the function $f(x) = 4x - 3$ when $x = 2$?

3

9

5

7

Feedback: Not quite! When $x = 2$, $f(2) = 4(2) - 3 = 4 \times 2 - 3 = 8 - 3 = 5$

Feedback: Well done! When $x = 2$, $f(2) = 4(2) - 3 = 4 \times 2 - 3 = 8 - 3 = 5$

3 / 6

Q: For the function $f(x) = 2x - 4$, what is the value of $f(3)$?

2

8

6

4

Feedback: Not quite! The "3" inside the brackets means we are replacing "$x$" with the value 3. So, $f(3) = 2(3) - 4 = 2 \times 3 - 4 = 2$

Feedback: Well done! The "3" inside the brackets means we are replacing "$x$" with the value 3. So, $f(3) = 2(3) - 4 = 2 \times 3 - 4 = 2$

4 / 6

Q: For the function $f(x) = 3x - 5$, what is $x$ when $f(x)$ is 7?

4

7

11

5

Feedback: Not quite! Substitute 7 for $f(x)$, so we have the equation: $7 = 3x - 5$. First, add 5 to both sides to get $12 = 3x$. Then, divide both sides by 3 to find $x = 4$.

Feedback: Well done! Substitute 7 for $f(x)$, so we have the equation: $7 = 3x - 5$. First, add 5 to both sides to get $12 = 3x$. Then, divide both sides by 3 to find $x = 4$.

5 / 6

Q: For the function $f(x) = 5x + 8$, what is the value of $f(-2)$?

-6

-8

-4

-2

Feedback: Not quite! To find $f(-2)$, substitute $x = -2$ into the function. So, $f(-2) = 5(-2) + 8 = -10 + 8 = -2$.

Feedback: Well done! To find $f(-2)$, substitute $x = -2$ into the function. So, $f(-2) = 5(-2) + 8 = -10 + 8 = -2$.

6 / 6

Q: Based on the graph, what are the values of $x$ when $f(x) = -3$?

$A graph of a quadratic function y = F(x) with marked points at x-values -4, -1, 1, and 5, showing corresponding y-values as peaks and valleys.$

5 and 1

2 and 0

3 and -1

4 and -2

Feedback: Not quite! From the graph, we can see that the function intersects the horizontal line $f(x) = -3$ at $x = 4$ and $x = -2$. Therefore, the correct answer is 4 and -2.

Feedback: Well done! From the graph, we can see that the function intersects the horizontal line $f(x) = -3$ at $x = 4$ and $x = -2$. Therefore, the correct answer is 4 and -2.

Your score is

The average score is 0%

0%

ChatCat (AI Math Solver)

Ask your math question at bottom right ⤵️

Courses Overview

Previous Lesson

Related

Log In

Username or Email Address

Password

Remember Me

Join Now | Lost Password?

Loading Comments...

Write a Comment...

Email (Required)

Name (Required)

Website

Login

Accessing this course requires a login. Please enter your credentials below!

Username or Email Address

Password

Remember Me

Lost Your Password?

Register

Don't have an account? Register one!

Register an Account