Lesson 3.3 Extra Practice
STUDENT BOOK PAGES 155–162
1. Given the graph of f (x) , graph the inverse relation.
a)
y
4
3
2
1
x
–4 –3 –2 –1 0
–1
–2
–3
–4
1
2 3 4
7. The height of a ball thrown from a balcony can be
modelled by the function
h(t) ⫽ ⫺5t 2 ⫺ 10t ⫹ 10, where h(t) is the
height above the ground, in metres, at time t
seconds after it is thrown.
a) Write h(t) in vertex form.
b) Determine the domain and range of h(t) .
c) Determine the model that describes time in
terms of the height.
d) What are the domain and range of the new
model?
8. Each graph shows a function f that is a parabola.
a)
y
4
3
2
1
y
b)
7
6
5
4
3
2
1
–2 –1 0
–1
–2 –1 0
–1
–2
–3
–4
x
1
2 3 4 5 6
x
1
2 3 4 5 6
y
Copyright © 2008 by Thomson Nelson
b)
2. Given the following equations, determine the
equation of the inverse.
a) f (x ) ⫽ x 2 ⫹ 8x ⫹ 16
b) f (x) ⫽ x 2 ⫺ 6x ⫹ 9
3. Given f (x) ⫽ 3 (x ⫹ 5 ) ⫺ 1, x ⱖ 1, determine
a) f (2)
b) f ⫺1 (x)
c) f ⫺1 (26)
2
4. Sketch a graph of f (x) ⫽ 2 (x ⫹ 4 ) 2. Sketch the
graph of its inverse on the same axes.
5. Given f (x) ⫽ 5x ⫺ 9, determine the equation for
f ⫺1 (x) . Graph the function and its inverse on the
same axes.
2
6. For f (x) ⫽ 5x 2 ⫹ 20x ⫹ 20 determine
a) the domain and range of f ⫺1 (x )
b) the equation of f ⫺1 (x) .
8
6
4
2
–4 –3 –2 –1 0
–1
–2
–3
–4
x
1
2 3 4
i) Determine f (x) .
ii) Graph f ⫺1 (x ) .
iii) State restrictions on the domain or range of f to
make its inverse a function.
iv) Determine the equation(s) for f ⫺1 (x) .
Lesson 3.3 Extra Practice
409