IB Mathematics Analysis and Approaches Topic SL 2.11—transformation of Functions Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 2.11—transformation of Functions Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 2.11—transformation of Functions with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 2.11—transformation of Functions and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 1

The graph of

y = f (x)

is shown below. The points

(- 1, 0)

and

(3, 0)

lie on the graph, with a minimum at

(1, - 2)

Sketch the graph of

y = \frac{1}{2} f (x)

on the diagram below.

[3]

The point $B (- 1, 0)$ is on the graph of $f$ . Find the coordinates of the corresponding point on the graph of $y = f (x + 3)$ .

[2]

Question 2

SLPaper 1

The function $f$ is defined by $f (x) = ln (4 x)$ , where $x > 0$ .

Calculate the exact value of $f (\frac{e ^{4}}{4})$ .

[2]

Calculate the exact value of $f (\frac{1}{4})$ .

[1]

Determine an expression for the inverse function $f^{- 1} (x)$ .

[4]

Using your result from part 3, or otherwise, calculate the value of $f^{- 1} (- 2)$ .

[1]

The graph of $y = f (\frac{e ^{3}}{4} x^{5})$ can be generated through a sequence of a vertical stretch and a vertical translation of the graph of $y = ln x$ . Describe these two transformations, clearly stating the order in which they should be performed.

[6]

Question 3

SLPaper 2

The basic function is $f (x) = x$ for $x \geq 0$ . Define the transformed function $g (x) = 3 x - 4 + 1, x \geq 4.$

Describe the transformations that map $y = f (x)$ to $y = g (x)$ .

[4]

State the domain and range of $g$ .

[2]

Solve $3 x - 4 + 1 = x - 2$ for $x \geq 4$ , giving your answers correct to 3 d.p.

[5]

Define $k (x) = ∣ g (x) ∣, x \geq 4$ . Using technology, solve $k (x) = x - 2$ for $4 \leq x \leq 13$ . Give all solutions correct to 3 d.p.

[5]

Question 4

SLPaper 2

The basic function is $f (x) = x$ for $x \geq 0$ . Define $g (x) = 1.5 x - 8 + 2, x \geq 8.$

Describe the transformations mapping $y = f (x)$ to $y = g (x)$ .

[4]

State the domain and range of $g$ .

[2]

Solve $1.5 x - 8 + 2 = \frac{1}{2} x - 1$ for $x \geq 8$ . Give exact values and values correct to 3 decimal places.

[5]

Question 5

SLPaper 1

Let $f (x) = 3 x^{2} - 12 x + 9$ , for $x \in R$ .

Write down the value of $f (0)$ .

[1]

Solve the equation $f (x) = 0$ .

[3]

The function $f$ can be written in the form $f (x) = a (x - h)^{2} + k$ .

Find the values of $a$ , $h$ and $k$ .

[3]

For the graph of $f$ , write down:

the coordinates of the vertex;

the equation of the axis of symmetry.

[2]

The graph of a function $g$ is obtained from the graph of $f$ by a reflection in the $x$ -axis, followed by a translation by the vector $(- 2 1)$ .

Find $g (x)$ , giving your answer in the form $g (x) = p x^{2} + q x + r$ .

[4]

IB Mathematics Analysis and Approaches SL 2.11—transformation of Functions Questionbank

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IB Mathematics Analysis and Approaches SL 2.11—transformation of Functions Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 2.11—transformation of Functions Questionbank

Unlock all 24 questions with a free account