Grade 12 Maths - Functions & Graphs Revision Worksheet

Instructions: Show all working including intercepts and turning points. Label all key points clearly on sketches. State the domain and range for each function.

Section A: Linear Functions (4 marks)

Given $f(x) = 2x - 6$:

1. Calculate the $x$-intercept. (1)

2. Calculate the $y$-intercept. (1)

3. Write down the gradient. (1)

4. Sketch the graph, labelling both intercepts. (1)

Section B: Quadratic Functions (8 marks)

Given $g(x) = -x^2 + 4x + 12$:

1. Determine the $x$-intercepts. (3)

2. Determine the $y$-intercept. (1)

3. Determine the coordinates of the turning point. (2)

4. Write down the equation of the axis of symmetry. (1)

5. Write down the range of $g$. (1)

Section C: Determine the Equation (4 marks)

A parabola has $x$-intercepts at $(-1; 0)$ and $(3; 0)$, and passes through the point $(1; 8)$.

Determine the equation of the parabola in the form $y = a(x-p)(x-q)$. (4)

Section D: Hyperbola (4 marks)

Given $h(x) = \dfrac{6}{x-2} + 1$:

1. Write down the equations of the asymptotes. (2)

2. Write down the domain and range. (2)

Total: 20 marks