Exercise Set 5.1: Exponential Functions
Graph each of the following functions by plotting
points. Show any asymptote(s) clearly on your graph.
1. x
xf 3)( =
2. x
xf 5)( =
3. x
xf 7)( =
4. x
xf 2)( =
5.
x
xf
=2
1
)(
6.
x
xf
=3
1
)(
7.
x
xf
=5
3
)(
8.
x
xf
=3
4
)(
Answer the following.
9. Based on your answers to 1-8 above:
(a) Draw a sketch of 1 where,)( >= aaxf x.
(b) Draw a sketch of .10 where,)( <<= aaxf x
(c) What point on the graph do parts (a) and (b)
have in common?
(d) Name any asymptote(s) for parts (a) and (b).
10. Based on your answers to 1-8 above:
(a) Draw a sketch of x
xf 7.2)( = without
plotting points.
(b) Draw a sketch of x
xf 73.0)( = without
plotting points.
(c) What point on the graph do parts (a) and (b)
have in common?
(d) Name any asymptote(s) for parts (a) and (b).
Graph each of the following pairs of functions on the
same set of axes.
11. xx xgxf 3)(,2)( ==
12. xx xgxf 7)(,4)( ==
13.
x
xxgxf
== 6
1
)(,6)(
14.
xx
xgxf
=
=5
2
)(,
2
5
)(
Sketch a graph of each of the following functions,
based on the concepts learned in numbers 1-10. (Note:
You do not need to plot points.) Be sure to label at
least one key point on your graph, and show any
asymptotes.
15. x
xf 8)( =
16. x
xf 12)( =
17. x
xf 2.0)( =
18. x
xf 3.0)( =
19. x
xf 2.9)( =
20. x
xf 4.1)( =
21.
x
xf
=2
7
)(
22.
x
xf
=8
3
)(
23.
x
xf
=11
9
)(
24.
x
xf
=4
9
)(
