Transforming Graphs y=f(x) - Worksheets, Questions and Revision

20 original exam-style questions - 10 pages of questions with a full mark scheme - free printable PDF.

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8.2 Transforming Graphs y=f(x)

EDEXCEL 1MA1 · Calculator allowed · about 90 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
The graph of y = g(x) is obtained from the graph of y = f(x) by a single translation. For each equation, write down the column vector that describes the translation from y = f(x) to y = g(x).
(a)g(x) = f(x) + 6(1)
(b)g(x) = f(x - 4)(1)
(c)g(x) = f(x + 2)(1)
(d)g(x) = f(x) - 5(1)
(Total for Question 1 is 4 marks)
2
The curve C has equation y = f(x). It has a minimum turning point at M(3, -4), crosses the x-axis at the points A(1, 0) and B(5, 0), and crosses the y-axis at the point D(0, 2).
(a)State the coordinates of the point on y = f(x) + 5 that corresponds to M.(1)
(b)State the coordinates of the point on y = f(x) + 5 that corresponds to A.(1)
(c)State the coordinates of the point on y = f(x) - 3 that corresponds to D.(1)
(d)State the coordinates of the point on y = f(x) - 3 that corresponds to B.(1)
(Total for Question 2 is 4 marks)
3
Using the same curve C as in Question 2 (minimum M(3, -4), x-intercepts A(1, 0) and B(5, 0), y-intercept D(0, 2)):
(a)State the coordinates of the point on y = f(x - 2) that corresponds to M.(1)
(b)State the coordinates of the point on y = f(x + 4) that corresponds to A.(1)
(c)The curve y = f(x - k) has a minimum point at (9, -4). Find the value of k.(2)
(Total for Question 3 is 4 marks)
4
The function h is defined by h(x) = x2 - 6x + 8.
(a)Find and simplify an expression for h(x - 3).(3)
(b)Hence write down the coordinates of the minimum point of y = h(x - 3).(2)
(Total for Question 4 is 5 marks)
5
Using the same curve C as in Question 2 (minimum M(3, -4), x-intercepts A(1, 0) and B(5, 0), y-intercept D(0, 2)):
(a)State the coordinates of the point on y = -f(x) that corresponds to M.(1)
(b)State the coordinates of the point on y = -f(x) that corresponds to D.(1)
(c)State the coordinates of the point on y = f(-x) that corresponds to M.(1)
(d)State the coordinates of the point on y = f(-x) that corresponds to B.(1)
(e)State which of the points A, B and D are invariant (stay in exactly the same position) under the transformation y = -f(x), and explain why.(2)
(Total for Question 5 is 6 marks)
6
Using the same curve C as in Question 2 (minimum M(3, -4), x-intercepts A(1, 0) and B(5, 0), y-intercept D(0, 2)), the curve y = f(x) is transformed to y = 3f(x).
(a)State the coordinates of the point corresponding to M.(1)
(b)State the coordinates of the point corresponding to D.(1)
(c)A student says: "The x-intercepts of y = 3f(x) are still x = 1 and x = 5." Is the student correct? Give a reason.(2)
(Total for Question 6 is 4 marks)
7
Using the same curve C as in Question 2 (minimum M(3, -4), x-intercepts A(1, 0) and B(5, 0), y-intercept D(0, 2)):
(a)State the coordinates of the point on y = f(2x) that corresponds to M.(1)
(b)State the coordinates of the point on y = f(x/2) that corresponds to A.(1)
(c)The curve y = f(kx) has a point corresponding to B at (2, 0). Find the value of k.(2)
(Total for Question 7 is 4 marks)
8
The graph of y = sin(x) for 0 ≤ x ≤ 360 has a maximum point at (90, 1), a minimum point at (270, -1), and passes through (0, 0), (180, 0) and (360, 0).
(a)State the coordinates of the maximum point of y = sin(x) + 2.(1)
(b)State the coordinates of the minimum point of y = sin(x) + 2.(1)
(c)Write down the range of y = sin(x) + 2.(2)
(Total for Question 8 is 4 marks)
9
The graph of y = cos(x) for 0 ≤ x ≤ 360 has a maximum at (0, 1), a zero at (90, 0), a minimum at (180, -1), a zero at (270, 0), and a maximum at (360, 1).
(a)State the coordinates of the point on y = cos(x - 60) that corresponds to the maximum at (0, 1).(1)
(b)State the coordinates of the point on y = cos(x - 60) that corresponds to the minimum at (180, -1).(1)
(c)State the coordinates of the point on y = cos(x - 60) that corresponds to the zero at (90, 0).(2)
(Total for Question 9 is 4 marks)
10
Answer the following multiple choice questions on graph transformations.
(a)The graph of y = f(x) is transformed to give the graph of y = f(x) + 4. Which of the following correctly describes this transformation?(1)
  • A) Translation by vector (4, 0)
  • B) Translation by vector (0, 4)
  • C) Translation by vector (-4, 0)
  • D) Translation by vector (0, -4)
(b)The graph of y = g(x) is transformed to give the graph of y = g(x - 5). Which of the following correctly describes this transformation?(1)
  • A) Translation by vector (5, 0)
  • B) Translation by vector (-5, 0)
  • C) Translation by vector (0, 5)
  • D) Translation by vector (0, -5)
(Total for Question 10 is 2 marks)
11
The function h is defined by h(x) = x2 - 8x + 10.
(a)Find h(x) + 9, giving your answer in the form x2 + bx + c.(2)
(b)Show that the equation h(x) + 9 = 0 has no real roots.(3)
(Total for Question 11 is 5 marks)
12
The curve y = p(x) has a maximum point at (4, 6).
(a)The curve y = p(x) + k has a maximum point at (4, -2). Find the value of k.(2)
(b)The curve y = p(x - a) has a maximum point at (10, 6). Find the value of a.(2)
(Total for Question 12 is 4 marks)
13
Using the same curve C as in Question 2 (minimum M(3, -4), x-intercepts A(1, 0) and B(5, 0), y-intercept D(0, 2)):
(a)State the coordinates of the point on y = f(x + 2) - 5 that corresponds to M.(2)
(b)State the coordinates of the point on y = f(x + 2) - 5 that corresponds to D.(2)
(Total for Question 13 is 4 marks)
14
Transformations can be described using column vectors.
(a)The graph of y = f(x) is translated by the vector (4, -7) to give the graph of y = g(x). Write down an expression for g(x) in terms of f(x).(2)
(b)The graph of y = f(x) is translated to give y = f(x + 3) + 2. Write down the column vector of this translation.(2)
(Total for Question 14 is 4 marks)
15
The curve y = q(x) is given by q(x) = x2 + 10x + 30.
(a)Express q(x) in the form (x + a)2 + b.(2)
(b)Hence, or otherwise, find the coordinates of the minimum point of the curve y = q(x - 4).(3)
(Total for Question 15 is 5 marks)
16
Using the same curve C as in Question 2 (minimum M(3, -4), x-intercepts A(1, 0) and B(5, 0), y-intercept D(0, 2)), the curve y = f(x) is transformed to y = -2f(x).
(a)State the coordinates of the point corresponding to M.(1)
(b)State the coordinates of the point corresponding to D.(1)
(c)Explain why A and B remain unchanged under this transformation, but M and D do not.(2)
(Total for Question 16 is 4 marks)
17
A curve y = r(x) passes through the point (8, 3).
(a)After the transformation y = r(x) + c, the image of this point is (8, -5). Find the value of c.(2)
(b)The curve y = r(kx) has an image point (2, 3) that corresponds to (8, 3) on y = r(x). Find the value of k.(2)
(Total for Question 17 is 4 marks)
18
The curve y = 1/x has asymptotes x = 0 and y = 0.
(a)State the equations of the asymptotes of the curve y = 1/(x - 3) + 2.(3)
(b)Hence write down the coordinates of the point on y = 1/(x - 3) + 2 that corresponds to the point (1, 1) on y = 1/x.(2)
(Total for Question 18 is 5 marks)
19
The curve y = f(x) has a line of symmetry x = 3.
(a)State the equation of the line of symmetry of the curve y = f(x - 2).(2)
(b)State the equation of the line of symmetry of the curve y = f(2x).(2)
(c)Explain why the curve y = f(x) + 7 has the same line of symmetry, x = 3, as the original curve.(1)
(Total for Question 19 is 5 marks)
20
The curve y = f(x) has a minimum point at (-2, 1). The curve y = g(x), where g(x) = f(x + a), has a minimum point at (3, 1). The curve y = h(x), where h(x) = f(x) + b, has a minimum point at (-2, 8).
(a)Find the value of a.(2)
(b)Find the value of b.(2)
(c)Using your values of a and b, write down the coordinates of the minimum point of the curve y = f(x + a) + b.(2)
(Total for Question 20 is 6 marks)
Mark scheme · 8.2 Transforming Graphs y=f(x)

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

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20