Transformations of Graphs of Functions - Worksheets, Questions and Revision

14 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

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IG.M11 Transformations of Graphs of Functions

EDEXCEL 4MA1 · Calculator allowed · about 40 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
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.
Figure (to be drawn): A set of coordinate axes is provided for sketching. Labelled point on original parabola: vertex (2, -3) and another point (0, 1). Student should sketch transformed parabola.
(Total for Question 1 is 1 mark)
2
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)
3
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.
Figure (to be drawn): Coordinate axes with the original cubic sketched crossing x-axis at -2, 0 and 3. The cubic shape should be evident (end behaviour not required in detail).
(Total for Question 3 is 2 marks)
4
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.
Figure (to be drawn): A sketch of a curve with a marked point A at (3, 2).
(Total for Question 4 is 2 marks)
5
Graph of y = f(x) has a minimum at (0, -5). State the coordinates of the minimum of y = f(2x).
(Total for Question 5 is 1 mark)
6
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 6 is 1 mark)
7
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 (to be drawn): 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 7 is 3 marks)
8
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 8 is 2 marks)
9
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 9 is 2 marks)
10
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.
Figure (to be drawn): Axes with the original parabola faintly shown; original vertex (1, 0) and point (0,1) labelled.
(Total for Question 10 is 2 marks)
11
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 11 is 2 marks)
12
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 (to be drawn): Axes from 0 to 2pi with faint cos x curve shown. Student to draw cos 2x and label relevant point.
(Total for Question 12 is 3 marks)
13
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 13 is 3 marks)
14
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 14 is 3 marks)
Mark scheme · IG.M11 Transformations of Graphs of Functions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14