A function is a special relationship where each input (x) has exactly one output (y). We use function notation like f(x) to represent this.
f(x) = 2x + 3
f(1) = 2(1) + 3 = 5
f(0) = 2(0) + 3 = 3
f(-2) = 2(-2) + 3 = -1
Domain: All possible x-values
Range: All possible y-values
Intercepts: Where graph crosses axes
Gradient: Slope of the line
Linear functions create straight line graphs with constant gradient.
Slope-intercept form: y = mx + c
m = gradient, c = y-intercept
Example: y = 3x - 2
Gradient = 3, y-intercept = -2
y = 2x + 1
Line slopes upward ↗
y = -x + 3
Line slopes downward ↘
Quadratic functions create parabola (curved) graphs.
f(x) = ax² + bx + c
f(x) = x² + 2x - 3
Parabola opens upward ∪
f(x) = -x² + 4x + 1
Parabola opens downward ∩
Functions can be transformed by shifting, stretching, or reflecting.
f(x) + k → shift up by k units
f(x) - k → shift down by k units
f(x + k) → shift left by k units
f(x - k) → shift right by k units
1. If f(x) = 3x - 2, find f(4)
2. What is the gradient of the line y = -2x + 5?