Methods2024 NHT Exam 2 Section B · Q4CAS active13 marks

Tiling pattern from transformations of a cubic

Timothy has created a tiling pattern using transformations of the cubic function

$f: [-4, 0] \to \R, f(x) = a(x-b)^3 + c$

The translation of $f$ given by $f_2(x) = f(x-4) - 4$ describes a different edge of one of the tiles.

Trace over the edge described by $f_2$ on the graph in Figure 1, and label this edge $f_2$ .

1 mark

Hints, answer checking and worked solutions come with a Season Pass.

Given that $f$ has a stationary point of inflection at $(-2, 2)$ and an axial intercept at $(0, 4)$ , find the values of $a$ , $b$ and $c$ .

2 marks

Hints, answer checking and worked solutions come with a Season Pass.

The piecewise function, $p$ , is continuous, where the first component is $f$ , the other component is a translation of $f$ and both are edges in Timothy's tiling pattern.

Complete a possible rule and domain for the second piece of the piecewise function $p$ .

$p(x) = \begin{cases} f(x) & -4 \le x \le 0 \\ \underline{\qquad\qquad} & \underline{\qquad\qquad} \end{cases}$

1 mark

Hints, answer checking and worked solutions come with a Season Pass.