Algebra and Graphs

Basic Expressions and Formulas

Introduction to Mapping

Introduction to Formulas

Deriving and Evaluating Expressions with One Variable

Equations and Simplifications

Simplifying Expressions

Solving Equations

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: Standard Form and Vertex Form

How to Write Quadratic Equations in Vertex Form and Standard Form

Solving Simple Quadratic Equations

Solving Quadratic Equations by Factorising

Solving Quadratic Equations: Quadratic Formula

Functions and Graphs

Plotting and Reflecting Points on the Coordinate Plane

Introduction to Functions and Graphs

Gradient and Y-Intercept in Linear Equations

Finding the Equation of a Straight Line

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Introduction to Functions and Graphs

Algebra and Graphs Introduction to Functions and Graphs

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(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) How to Graph a Function?: Start by creating a table of input-output pairs (e.g., $f(1) = 3$, $f(2) = 5$). Then, plotting these points on a graph makes it easier to interpret.
(1:31) Key Characteristic of Functions:In a function, a single x-value cannot be paired with multiple y-values. However, the same y-value can be assigned to different x-values.
(2:17) Finding Function Values from Graphs: To find $f(a)$, locate $x = a$ on the graph and read the corresponding y-value.

📂 Revision Cards

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

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) Practice: Function Definition

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 Time - Practice Now!

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Introduction to Functions and Graphs

1 / 6

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

23

20

17

15

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 $x = 2$?

5

9

7

3

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 $f(3)$?

8

4

2

6

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?

11

4

7

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

-4

-8

-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 $f(x) = -3$?

3 and -1

4 and -2

5 and 1

2 and 0

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.

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