Introduction to Functions: Types and Notation
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Introduction to Functions: Types and Notation
Year 11 Mathematics Understanding the Building Blocks of Advanced Algebra
What is a Function?
Think about a vending machine... You put in £1, you get one chocolate bar Input → Rule → Output Can you think of other real-life examples?
Formal Definition of a Function
A function assigns exactly ONE output to each input from its domain Domain: all possible input values (x-values) Range: all possible output values (y-values) Function notation: f(x) = 'f of x' The rule that transforms input x into output y
Linear Functions
Form: f(x) = mx + c m = gradient (slope) c = y-intercept Graph: straight line Example: f(x) = 2x + 3
Quadratic Functions
Form: f(x) = ax² + bx + c a determines if parabola opens up or down Graph: U-shaped curve (parabola) Has a turning point (vertex) Example: f(x) = x² - 4
Exponential Functions
Form: f(x) = aˣ (where a > 0, a ≠ 1) Shows rapid growth or decay Graph: curved line that never touches x-axis Always positive output values Example: f(x) = 2ˣ
Function Sorting Challenge
Work in groups of 5 Match algebraic expressions to their graphs Classify each function type: Linear, Quadratic, or Exponential Evaluate f(x) for given x-values Sketch your chosen function on graph paper
Key Takeaways
Functions assign exactly one output to each input Three main types: Linear (straight line), Quadratic (parabola), Exponential (curved growth/decay) Function notation f(x) helps us work with mathematical relationships Domain and range describe input and output possibilities Functions appear everywhere in mathematics and real life