(a)[1]
Complete the table shown below.
(b)[2]
On a scale where $2\text{ cm}$ represents $1$ unit, draw a horizontal $x$-axis for $-3 \le x \le 3$. On a scale where $2\text{ cm}$ represents $10$ units, draw a vertical $y$-axis for $-30 \le y \le 30$. Using these axes, plot the points in the table and link them with a smooth curve.
(c(i))[1]
Use your graph to solve $f(x) = -15$.
(c(ii))[1]
Use your graph to find the value of $a$ such that $f^{-1}(a) = 1.7$.
(c(iii))[1]
Given that $f^{-1}(t) = u$, write $t$ in terms of $u$.
(c(iv))[2]
By sketching a tangent to $y = f(x)$, estimate the gradient of the curve at $x = 2$.
(d(i))[2]
On the same axes, draw the line that represents the function $g(x) = 5x + 3$.
(d(ii))[2]
Hence, find the three solutions to the equation $f(x) = g(x)$.