IB Mathematics Applications & Interpretation Topic AHL 2.8—transformations of Graphs, Composite Transformations Questionbank (HL)

IB Mathematics Applications & Interpretation Topic AHL 2.8—transformations of Graphs, Composite Transformations Questionbank (HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 2.8—transformations of Graphs, Composite Transformations with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 2.8—transformations of Graphs, Composite Transformations and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 1

Let $f (x) = 2 x + 1$ .

Draw the graph of $f (x)$ for $0 \leq x \leq 2$ .

[3]

Let $g (x) = 2 x + 5$ . Draw the graph of $g (x)$ for $- 3 \leq x \leq - 1$ .

[3]

Question 2

SLPaper 1

Let $f (x) = x^{2} + 4$ and $g (x) = x - 1$ .

Find $(f \circ g) (x)$ .

[2]

The translation by the vector $(- 1 3)$ maps the graph of $(f \circ g) (x)$ to the graph of $h$ . Find the vertex of $h$ .

[3]

Show that $h (x) = x^{2} - 8 x + 19$ .

[2]

The line $y = 2 x - 6$ is tangent to $h$ at the point $P$ . Find the $x$ -coordinate of $P$ .

[3]

The line $y = 2 x - 5$ intersects the graph of $h$ at two points. Find the coordinates of the two points of intersection.

[4]

Question 3

SLPaper 1

The figure shows a portion of the graph of

f (x) = 4 - x^{2}

, with vertex

V (0, 4)

, drawn in black. After a translation by the vector

(k h)

, its image

y = g (x)

has vertex

T (2, 7)

, drawn in blue.

Write down the value of $h$ and the value of $k$ .

[2]

Write down a formula for $g (x)$ .

[3]

On the same diagram, sketch the graph of $y = g (- x)$ .

[2]

Question 4

HLPaper 1

Given $h (x) = x + 1$ .

This function is transformed to produce various other functions.

Write down the equation of $j (x)$ if it represents $h (x)$ reflected in the $x$ -axis.

[2]

Write down the equation of $g (x)$ if it represents $h (x)$ reflected in the $y$ -axis.

[2]

Describe the transformations applied to $h (x)$ to obtain $f (x) = - - x + 1$ .

[2]

Question 5

HLPaper 2

A temperature sensor has a response curve $y = f (x)$ , where $x$ is the temperature in $^{\circ} C$ and $y$ is the output signal in mV. After recalibration, the relationship is modelled by $y = 2 f (x - 3) + 4$ .

The point $A (- 1, 3)$ lies on the curve $y = f (x)$ .

Describe the effect of the transformation $y = f (x - 3)$ on the graph of $y = f (x)$ .

[2]

Describe the effect on the $y$ -coordinates of multiplying by 2 and then adding 4, as in $y = 2 f (x) + 4$ .

[2]

Find the coordinates of the image of $A$ on the graph of $y = 2 f (x - 3) + 4$ .

[4]

Determine the coordinates of the point on $y = f (x)$ that corresponds to the point $(5, 14)$ on the graph of $y = 2 f (x - 3) + 4$ .

[4]

IB Mathematics Applications & Interpretation AHL 2.8—transformations of Graphs, Composite Transformations Questionbank

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IB Mathematics Applications & Interpretation AHL 2.8—transformations of Graphs, Composite Transformations Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 2.8—transformations of Graphs, Composite Transformations Questionbank

Unlock all 25 questions with a free account