IB Maths AA HL Ahl 2 16 Hl Further Graph Transformations Questions

Practise transforming graphs with modulus, reciprocal, square and horizontal-scale operations, then solving resulting modulus equations or inequalities within the domain.

Exam points

Apply further graph transformations, including combinations of translations, stretches and reflections.
Determine transformed equations and key features from complex transformations using complete evidence.

[Maximum number: 3]

Consider the function $f(x)=a x^{3}+b x^{2}+c x+d$ , where $x \in \mathbb{R}$ and $a, b, c, d \in \mathbb{R}$ .

Consider the function $g(x)=\frac{1}{2} x^{3}-3 x^{2}+6 x-8$ , where $x \in \mathbb{R}$ .

$\quad g(x)$ can be written in the form $p(x-2)^{3}+q$ , where $p, q \in \mathbb{R}$ . Find the value of p and the value of q.

$\quad p=\frac{1}{2}$

\begin{aligned} & (x-2)^{3}=x^{3}-6 x^{2}+12 x-8 \\ & \frac{1}{2}\left(x^{3}-6 x^{2}+12 x-8\right)=\frac{1}{2} x^{3}-3 x^{2}+6 x-4 \\ & g(x)=\frac{1}{2}(x-2)^{3}-4 \Rightarrow q=-4 \end{aligned}

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IB Maths AA HL Ahl 2 16 Hl Further Graph Transformations Questions question 1