Write down the coordinates of the image of this point on each of these graphs.
y = f(x + 3)
y = f(x) − 4
y = −f(x)
y = f(−x)
4 marks
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a) (-1, 5)b) (2, 1)c) (2, -5)d) (-2, 5)
2
The point (6, −4) lies on the graph of y = f(x).
Write down the coordinates of the image of this point on each of these graphs.
y = 2f(x)
y = f(2x)
y = f(13x)
y = −3f(x)
4 marks
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a) (6, -8)b) (3, -4)c) (18, -4)d) (6, 12)
3
The point A(−2, 3) lies on the graph of y = f(x).
Write down the coordinates of the image of A on each of these graphs.
y = f(x − 3) + 1
y = −f(x + 1)
y = 2f(x) − 1
y = f(2x) + 5
4 marks
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a) (1, 4)b) (-3, -3)c) (-2, 5)d) (-1, 8)
4
The graph of y = f(x) has a turning point at (3, −5).
Write down the coordinates of the turning point of the graph of y = f(x) + 4
Write down the coordinates of the turning point of the graph of y = f(x − 2)
2 marks
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a) (3, -1)b) (5, -5)
5
The point A (4, 7) lies on the graph of y = f(x).
Find the coordinates of the image of A on the graph of y = f(−x)
Find the coordinates of the image of A on the graph of y = −f(x)
2 marks
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a) (-4, 7)b) (4, -7)
6
The graph of y = sin x for 0° ≤ x ≤ 360° has a maximum point at (90, 1).
Write down the coordinates of the maximum point of the graph of y = sin x − 3
Write down the coordinates of the maximum point of the graph of y = sin (x − 30°)
2 marks
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a) (90, -2)b) (120, 1)
7
The graph of y = f(x) passes through the point (2, 5).
Write down the coordinates of a point that must lie on the graph of y = f(x + 6)
Write down the coordinates of a point that must lie on the graph of y = f(x) − 2
2 marks
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a) (-4, 5)b) (2, 3)
8
Describe fully the single transformation that maps the graph of y = x2 onto the graph of y = (x + 4)2
Describe fully the single transformation that maps the graph of y = x2 onto the graph of y = −x2
2 marks
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a) translation by the vector (-4, 0), i.e. 4 units to the leftb) reflection in the x-axis
9
The graph of y = cos x is drawn for 0° ≤ x ≤ 360°.
The graph of y = cos x + 2 is sketched on the same axes for 0° ≤ x ≤ 360°.
Write down the coordinates of the minimum point of y = cos x + 2
Write down the coordinates of the maximum point of y = cos x + 2 with the smallest x-coordinate
2 marks
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a) (180, 1)b) (0, 3)
10
The curve C has equation y = f(x) where f(x) = x2 + 2x.
Curve A is the reflection of C in the y-axis. Find the equation of curve A in the form y = x2 + bx + c
Curve B is the translation of C by 3 units in the positive y direction. Find the equation of curve B.
3 marks
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a) y = x2 - 2xb) y = x2 + 2x + 3
11
The graph of y = f(x) has a maximum point at (−1, 4) and crosses the x-axis at (−3, 0) and (1, 0).
Write down the coordinates of the minimum point of the graph of y = −f(x)
Write down the coordinates of the maximum point of the graph of y = f(x − 2)
Write down the coordinates of the points where the graph of y = f(x − 2) crosses the x-axis.
3 marks
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a) (-1, -4)b) (1, 4)c) (-1, 0) and (3, 0)
12
f(x) = x2 − 4x + 7
Write f(x) in the form (x − a)2 + b and hence write down the coordinates of the turning point of y = f(x)
Write down the coordinates of the turning point of y = f(x − 3)
Find the equation of y = f(−x), giving your answer in the form y = x2 + bx + c
4 marks
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a) f(x) = (x - 2)2 + 3; turning point (2, 3)b) (5, 3)c) y = x2 + 4x + 7
13
The diagram shows the graph of y = sin x for 0° ≤ x ≤ 360°.
On the same axes, sketch the graph of y = sin x − 2 for 0° ≤ x ≤ 360°
The point P (30, 0.5) lies on the graph of y = sin x. P is mapped to the point Q on the graph of y = sin (x − 60°). Find the coordinates of Q.
4 marks
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a) the sine curve translated 2 units down: through (0, -2), maximum (90, -1), (180, -2), minimum (270, -3), (360, -2)b) (90, 0.5)
14
f(x) = cos x° for all real values of x
Write down the coordinates of the minimum point of the graph of y = f(x) + 2
Write down the coordinates of the maximum point of the graph of y = f(x − 30) for 0 ≤ x ≤ 360
The graph of y = f(x) is reflected in the x-axis. Write down the equation of the reflected graph.
4 marks
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a) (180, 1)b) (30, 1)c) y = -cos x
15
Describe fully the single transformation that maps the graph of y = f(x) onto the graph of
y = f(x) + 5
y = f(x − 4)
y = −f(x)
y = f(2x)
y = 3f(x)
5 marks
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a) translation by vector (0, 5)b) translation by vector (4, 0)c) reflection in the x-axisd) stretch, scale factor 1/2, parallel to the x-axise) stretch, scale factor 3, parallel to the y-axis
16
The graph of y = tan x° passes through (45, 1) and has an asymptote at x = 90.
The graph of y = tan x° is reflected in the x-axis and then translated 30 to the right and 2 up. This gives the graph C with equation y = −tan(x − 30)° + 2.
Write down the coordinates of the image of (45, 1) on C.
Write down the equation of the image of the asymptote x = 90 on C.
Write down the y-coordinate of the point on C where x = 30.
4 marks
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a) (75, 1)b) x = 120c) 2
17
f(x) = x2 − 4x
Write f(x + 1) in the form x2 + ax + b.
The graph of y = f(x) has its minimum point at (2, −4). Write down the minimum point of y = f(x + 1).
4 marks
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a) x2 - 2x - 3b) (1, -4)
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.