Exam-Style Questions.

The images below show a graphic display calculator screen with different functions displayed as graphs.

a) Which function is trigonometric?

b) Which function is inversely proportional to \(x\)?

c) Which function is exponential?

d) Which function is proportional to \(x^3\)?

Worked Solution

Match the equation with the letter of its graph

Worked Solution

The graph of y = f(x) is drawn accurately on the grid.

(a) Write down the coordinates of the turning point of the graph.

(b) Write down estimates for the roots of f(x) = 0

(c) Use the graph to find an estimate for f(-5.5).

Worked Solution

Part of the function of \(y=f(x)\) is shown in the following diagram.

(a) Write down the value of \(f(1)\).

(b) Write down the value of \(ff(7)\).

(c) Sketch the graph of \(g(x)\) if \(g(x) = -f(x)-1\) on the same set of axes above.

Worked Solution

A function is defined as \(f(x) = 2{(x - 3)^2} - 5\) .

(a) Show that \(f(x) = 2{x^2} - 12x + 13\).

(b) Write down the equation of the axis of symmetry of this graph.

(c) Find the coordinates of the vertex of the graph of \(f(x)\).

(d) Write down the y-intercept.

(e) Make a sketch the graph of \(f(x)\).

Let \(g(x) = {x^2}\). The graph of \(f(x)\) may be obtained from the graph of \(g(x)\) by the two transformations:

• a stretch of scale factor \(s\) in the y-direction;
• followed by a translation of \(\left( {\begin{array}{*{20}{c}} j\\ k \end{array}} \right)\) .

(f) Find the values of \(j\), \(k\) and \(s\).

Worked Solution

Let \(f(x) = \frac{9x-3}{bx+9}\) for \(x \neq -\frac9b, b \neq 0\).

(a) The line \(x = 3\) is a vertical asymptote to the graph of \(f\). Find the value of b.

(b) Write down the equation of the horizontal asymptote to the graph of \(f\).

(c) The line \(y = c\) , where \(c\in \mathbb R\) intersects the graph of \( \begin{vmatrix}f(x) \end{vmatrix} \) at exactly one point. Find the possible values of \(c\).

Worked Solution