IB Maths AA HL 2.16 Further graph transformations Question Bank

Practise IB Mathematics HL 2.16 by applying further graph transformations methods to exam-style questions.

Exam points

[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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