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Exponential Functions
Simplify the
following. Express final answer with positive exponents
1
3
p q
p
4
8
2 7 3
5 4 5
b a y
a b y
2
4
z 3 z
z 2 z
4 4
2 1
1
2
n
n
a
a
Without using a log function find the value of the variable
x
x
2
x
Solve the equation
- 6 5 6 0
2
x x
x
Writing equations from a graph
- Each of the graphs below represents a function of the form
x
y Cb , with
b 0
b 1
. In
each case, write a formula for the function.
- Determine an equation of the form
x
y Cb , with
b 0
b 1
, so that the graph passes
through the points
a) (0, 5) and (1,15) b) (0, 8) and (4, 2) c) (1, 12) and (3, 192)
Algebra Review of exponents
a b a b
x x x
x h x h
b b b
mn
n
m
x
x
x
mn
n
m
x x
1
x
x
2
1
x x
3
1
3
x x
n
m
n
x x
m
If
x y
b b then
x y
- The tables below give the function values for two functions,
f ( x )
and
g ( x )
. One of the
functions is linear; the other is exponential. Determine which function is which (show work on
how you decided) then write an equation for each
x 1 2 3 4
f ( x )
x
g ( x )
- Determine an equation of the form
x
y Cb , with b 0 , b 1 , so that the graph passes
through the points
a) (0, -7) and (1,-
9 ) b) (0, 4096) and (4, 1) c) (-1,
) and (2, 15.75)
26. Determine if function in the tables illustrate an exponential function in the form
x
y Cb ,
linear function in the form
y mx b , or neither.
If exponential or linear write the formula for the function.
If neither, state how you know, either with a valid reason or by showing it is not linear or
exponential. An invalid reason is it is not linear therefore must be exponential
[Do not use the linear or exponential regression line on your calculator]
a)
27. Find a formula for each graph.
A. Contains the points (0, 1.5) and (2, 0.4374) B. Contains the points (-2, 0.48) and
x
f ( ) x
x
h x ( )
x
g x ( )
x
k ( x )
0
5
10
15
20
-2 -1 0 1 2 3
x
0
10
20
30
40
50
60
-2 -1 0 1 2 3
x
