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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.

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📂 Revision Cards

Diagram explaining that a function transforms an "input" to one "output."

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

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

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.

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

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