Transformations of Graphs of Functions - Worksheets, Questions and Revision

14 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 6)Transformations of Graphs of Functions revision guide

This topic is chapter 7 of IGCSE Maths Practice Book 1.

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2.6 Transformations of Graphs of Functions

EDEXCEL 4MA1 · Calculator allowed · about 40 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

The graph of y = f(x) is a parabola with vertex at (2, -3) and passes through (0, 1). Sketch the graph of y = f(x) + 4 on the same axes and label the new vertex coordinate.

(Total for Question 1 is 1 mark)

The graph of y = f(x) has a maximum at (-1, 2). Write down the coordinates of the minimum of y = -f(x).

(Total for Question 2 is 1 mark)

Graph of y = f(x) has a minimum at (0, -5). State the coordinates of the minimum of y = f(2x).

(Total for Question 3 is 1 mark)

The graph of y = f(x) has an x-intercept at (4, 0). State the x-intercept of y = f(x + 3).

(Total for Question 4 is 1 mark)

The graph of y = f(x) is a parabola with vertex at (1, 0) and passes through (0, 1). Sketch the graph of y = 2 - f(x) on the same axes and label the new vertex coordinate.

(Total for Question 5 is 2 marks)

The graph of y = f(x) has a maximum at (-1, 4). State the coordinates of this maximum after the transformation y = f(3x). Explain briefly.

(Total for Question 6 is 2 marks)

A cubic curve y = f(x) has x-intercepts at x = -2, 0 and 3. Sketch the graph of y = f(x - 1) and state the new x-intercepts.

(Total for Question 7 is 2 marks)

The graph of y = f(x) is shown and has a labelled point A at (3, 2). Describe the single transformation that maps the graph of y = f(x) onto the graph of y = 2 f(x). Also write down the coordinates of the image of A.

(Total for Question 8 is 2 marks)

The graph of y = f(x) has a point B at (-2, 3). Describe the single transformation that maps y = f(x) onto y = f(x) - 2, and write down the coordinates of the image of B.

(Total for Question 9 is 2 marks)

Point C is on the graph of y = f(x) at C = (1, -4). State the image of C under the transformation y = -f(x) + 1. Give a brief reason.

(Total for Question 10 is 2 marks)

Sketch y = cos(2x) for 0 ≤ x ≤ 2pi on the same axes as y = cos x (faint). State the x-coordinate of the first positive x where cos(2x) = 1.

Figure: Axes from 0 to 2pi with faint cos x curve shown. Student to draw cos 2x and label relevant point.

(Total for Question 11 is 3 marks)

A point D on y = f(x) is at D = (2, -1). Find the image of D under the transformation y = 0.5 f(x + 2) - 3. Give a brief explanation of each step.

(Total for Question 12 is 3 marks)

The graph of y = f(x) has a labelled point E at (4, -1). State the image of E under the single transformation that maps y = f(x) to y = 3 f(x - 2) + 5. Give a brief reason.

(Total for Question 13 is 3 marks)

A trig graph y = f(x) = sin x has a maximum at P at x = π/2 with coordinates (π/2, 1). Sketch y = sin(x/2) on the same axes for 0 ≤ x ≤ 4pi and write down the x-coordinate of the first maximum to the right of x = 0.

Figure: Axes from x = 0 to x = 4pi labelled, with original sin x curve faintly shown and point P at (π/2, 1).

(Total for Question 14 is 3 marks)

Mark scheme · 2.6 Transformations of Graphs of Functions

Question 1

B1 sketch shows parabola shifted vertically up by 4 with correct orientation and position, and new vertex labelled (2, 1) cao
Answer: New vertex (2, 1)

Question 2

B1 minimum is at (-1, -2) cao
Answer: (-1, -2)

Question 3

B1 minimum remains at x = 0 with same y, so (0, -5) cao
Answer: (0, -5)

Question 4

B1 x-intercept is at (1, 0) cao
Answer: (1, 0)

Question 5

M1 sketch shows reflection in x-axis of original parabola and a translation up by 2 units, preserving shape
A1 new vertex labelled at (1, 2) cao
Answer: New vertex at (1, 2)

Question 6

M1 recognition that x-coordinate changes by factor 1/3 for points not at x = 0, or that maxima x coordinate becomes -1/3
A1 coordinates (-1/3, 4) cao
Answer: (-1/3, 4)

Question 7

M1 sketch shows the cubic shifted right by 1, preserving shape and relative turning points
A1 new x-intercepts written as -1, 1 and 4 cao
Answer: x-intercepts: -1, 1 and 4

Question 8

M1 correct description: stretch vertically by a factor of 2 with respect to the x-axis, oe
A1 coordinates of image given as (3, 4) cao
Answer: Stretch vertically by factor 2 in the y-direction; A maps to (3, 4)

Question 9

M1 description: translate vertically down by 2 units (or shift down 2), oe
A1 image coordinates (-2, 1) cao
Answer: Translate down 2 units; B maps to (-2, 1)

Question 10

M1 correct image coordinates (1, 5) stated
A1 brief reason: reflect in x-axis then translate up 1 so y = -(-4) + 1 = 5, oe
Answer: (1, 5)

Question 11

M1 sketch shows horizontal compression with period π and correct amplitude 1
M1 shows cos(2x) = 1 at x = 0 and at least one further positive x correctly placed
A1 first positive x where cos(2x)=1 given as x = π
Answer: First positive x where cos(2x) = 1 is x = π

Question 12

M1 correctly applies horizontal translation: x comes from solving x + 2 = 2 so original x for image is 0, or explains point mapping: point (2, -1) on f corresponds to x = 2, so for f(x + 2) the same y occurs at x = 0
M1 applies vertical scale and translation: y = 0.5*(-1) - 3 = -0.5 - 3
A1 final coordinates (0, -3.5) cao
Answer: (0, -3.5)

Question 13

M1 recognises horizontal shift right by 2: x = 4 becomes x = 6
M1 applies vertical stretch factor 3 then translation up 5: y = -1 -> 3 * (-1) + 5 = 2
A1 final image (6, 2) cao
Answer: (6, 2)

Question 14

M1 sketch shows horizontal stretch by factor 2 with doubled period, peaks at correct relative positions, and correct amplitude 1
M1 student shows at least one maximum at x = π with correct labelling or peak location ft their sketch
A1 first maximum to the right of 0 stated as x = π cao
Answer: First maximum at x = π

Transformations of Graphs of Functions - Worksheets, Questions and Revision

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2.6 Transformations of Graphs of Functions

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