Exercises 1
These are examples of the simpler functions. Write their equations.
1
2
3
4
5
6
Page 1
Exercises 2
More examples of the simpler functions to write equations.
7
8
9
10
11
12
Page 2
Exercises 3
Write with the correct limits on domain.
13
14
15
16
17
18
Page 3
Exercises 4
Examples with different scales.
19
20
21
22
23
24
Page 4
Exercises 5
Write the equations for these functions. Many involve fractional multipliers.
25
26
27
28
29
30
Page 5
Exercises 6
Write the equations for these functions.
31
32
33
34
35
36
Page 6
Exercises 7
Write the equations for these exponential functions.
37
38
39
40
41
42
Page 7
Exercises 8
Write the equations for these exponential or log functions.
43
44
45
46
47
48
Page 8
Extension Exercises 1
Excellence questions on Exponential functions.
1
2
3
4
5
6
Page 9
Extension Exercises 2
Write the equations for these exponential and log functions.
7
8
9
10
11
12
Page 10
Extension Exercises 3
Write the equations for these exponential functions.
13
14
15
16
17
18
Page 11
Extension Exercises 4
Write the equations for these log functions.
19
20
21
22
23
24
Page 12
Answers
Fractions can replace decimals. Brackets can be in any order.
Exercises 1
Exercises 5
1
y = √𝑥 + 2 – 1
25
y = 2 (x – 2)2 – 4
2
y=2|x–2|–1
26
y = 2 |x + 3 | – 2
3
y = (x + 2) x or y = (x + 1)2 – 1
27
y = 3 √𝑥 + 1 – 1
4
y = 0.25(x + 2)(x – 1)(x – 2)
28
y = −1
(x – 1)2 + 3 (or use intercepts)
3
5
y = –2 (x – 1)2 + 3
29
2
y = 𝑥+
1 +2
6
y=5|x+1|–3
30
y=–3|x–2|+4
Exercises 2
Exercises 6
7
y = 2 √𝑥 − 1 – 2
31
y = 0.5 √𝑥 + 3 + 2
8
y = 2 (x +1)(x – 1)2
32
y = 𝑥−3
−1 + 1
9
y = 41 (x + 4) x or y = 41 (x + 2)2 – 1
33
y = 34 (x + 2)2 + 1
10
y = –0.5 | x + 2 | + 3
34
y = 0.5 | x + 2 | + 1
11
y = –0.5 √𝑥 + 3 + 2
35
y = -2 √𝑥 − 1 + 4
12
y = 1𝑥 + 1
36
1
y = 𝑥0.5
+ 2 – 1 or y = 2𝑥 + 4 – 1
Exercises 3
Exercises 7
x
13
y = x (x – 1)(x – 3)
for 0 ≤ x ≤ 3
37
y=3
14
y=|x+1|–3
for –3 < x < 1
38
y=2
15
y = –2 (x – 2)2 + 3
for 1 ≤ x ≤ 3
39
y=2 +2
16
y = 4 (x + 2)2 – 1
for –3 < x < –1
40
y=2
17
y = 2𝑥
for x > 0
41
y = 0.25
18
y = 31 (x + 2) x (x – 3) for –2 ≤ x ≤ 3
42
y = 0.5
x–2
x
x–1
–2
x
x+2
Exercises 4
Exercises 8
19
y = 0.25 x (x – 4)(x – 8)
43
y=2
20
y = 0.2 x (x – 10)2
44
y = log10(x – 1)
21
y = 16
𝑥 –4
45
y=3
22
y = –4 | x – 8 | + 16
46
y = 3 log10(x)
23
y = 2 √𝑥
47
y = 0.25 – 4
24
y = –0.2 x (x – 15)
48
y = log10(x + 2) + 3
Page 13
x–1
x+1
+3
–3
x
Extension Answers
Extension Exercises 1
x
1
y=5
2
y=2 +2
3
y = 0.2
4
y=3
5
y = 0.5 + 2
6
y=2
x
x
y = ( 51 )
x
or
x+1
–3
x
x–2
Extension Exercises 2
7
x
y = ( 31 ) – 1 – 1
8
y = log10(x – 1) + 3
9
y=3
10
y = log2(x – 2) or y =
11
y=2
12
y = log3(x + 2) – 2 =
x–1
x+3
–2
log (𝑥 − 2)
log (2)
–4
log (𝑥 + 2)
–2
log (3)
Extension Exercises 3
x
13
y=2 –3
14
y = 0.5
15
y=2
16
y = 0.25
17
y = 3 × 2 – 1 (or similar)
18
y = 5 × 0.5 + 1 (or similar)
x+1
x+2
+2
–1
x–1
–2
or
x
y = ( 41 ) – 1 – 2
x
x
Extension Exercises 4
19
y = log10(x – 1)
20
y = log10(x) – 1
21
y = log3(x + 2) =
70
71
72
log (𝑥 + 2)
log (3)
log (𝑥 − 1)
y = log2(x – 1) = log (2)
log (𝑥 + 2)
y = log4(x + 2) – 2 = log (4) – 2
log (𝑥 − 1)
y = log2(x – 1) + 3 = log (2) + 3
Page 14