Sketching Graphs Worksheet
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1Sketching Graphs
1) The first graph shown below is the graph of y = f(x). The other 7 graphs are transformations of this. Match each with the correct
equation from the following list:
(i) y = f(x + 3)
(ii) y = f(x) – 3
(iii) y = –f(x)
(iv) y = 3 – f(x) (v) y = f(–x)
(vi) y = ½f(x)
(vii) y = f(2x)
4
4
4
4
y
y
y
y
2
2
2
2
x
x
x
x
−4
−2
2
4
−4
−2
2
4
−4
−2
2
4
−4
−2
2
4
−2
−2
−2
−2
−4
−4
−4
−4
A
B
C
4
4
4
4
y
y
y
y
2
2
2
2
x
x
x
x
−4
−2
2
4
−4
−2
2
4
−4
−2
2
4
−4
−2
2
4
−2
−2
−2
−2
−4
−4
−4
−4
D
E
F
G
2) Using the same graph for y = f(x) as in question 1, sketch each of the following, indicating the coordinates of any significant
points:
(a) y = f(x – 2)
(b) y = f(x) – 2
(c) y = 2f(x)
(d) y = f(x)
(e) y = f(x + 3) + 2
3) Below are 8 graphs labelled A to H. These are graphs of the eight equations shown below. Match each graph with the correct
equation.
(i) y = (x – 2)(x + 3)
(ii) y = 3 – x
2
(iii) y = x
3
+ 3
(iv) y = 3x – x
2
6
(v) y = (x + 2)
2
(vi) y =
(vii) y = (x + 2)(x –1)(x –3)
(viii) y = (x – 2)
2
+ 3
x
20
20
20
y
20
y
y
y
10
10
10
10
x
x
x
x
−5−4−3−2−1
1 2 3 4 5
−5−4−3−2−1
1 2 3 4 5
−5−4−3−2−1
1 2 3 4 5
−5−4−3−2−1
1 2 3 4 5
−10
−10
−10
−10
−20
−20
−20
−20
A
B
C
D
20
20
20
y
20
y
y
y
10
10
10
10
x
x
x
x
−5−4−3−2−1
1 2 3 4 5
−4
−2
2
4
−5−4−3−2−1
1 2 3 4 5
−5−4−3−2−1
1 2 3 4 5
−10
−10
−10
−10
−20
−20
−20
−20
E
F
G
H
4) Sketch the graph of each of the following equations:
12
(a) y = (x –4)(x + 3)
(b) y = 5 – x
3
(c) y = (x + 3)
2
+ 2
(d) y = –
(e) y = x(4 – x)
x
12
(f) y =
(g) y = 9 – x
2
(h) y = + 2
(i) y = x
2
+ x – 6
(j) y = (x + 2)(x –3)(x – 5)
x+ 2
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