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

Sketch y=|f(x)| by reflecting negative sections in the x-axis and mark new intercepts or cusps.
Sketch y=f(|x|) by copying the appropriate half of f and state the resulting domain/intercepts or solution set.
Analyse y=1/f(x), y=[f(x)]Â² or y=|f(|x|)| by tracking excluded values, asymptotes, zeros and branch behaviour.
Apply f(ax+b) and related ordered transformations to derive or sketch the graph with the correct horizontal scale, translation and reflection.
Solve modulus equations or inequalities graphically or analytically, splitting cases and rejecting values outside the stated domain.

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Study AHL 2.16 (HL)—Further graph transformations conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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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