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Chapter 8 Study Sheet
I. Exponential Functions:
A. An exponential function has the form y = __________.
B. If the function f(x) = abx has a > 0 and b > 1, then it is an example of an exponential
______________ function.
C. If the function f(x) = abx has a > 0 and 0 < b < 1, then it is an example of an exponential
_________________ function.
D. For exponential growth functions, the line __________ is an asymptote for the parent graph.
E. State whether the following are true or false for y = abx (where a ≠ 0, b > 0, b ≠ 1):
1. The function is continuous and one-to-one.
2. The range is the set of all real numbers.
3. The x-axis is an asymptote of the graph.
4. The graph contains the point (0, a) (i.e. ‘a’ is the y-intercept).
5. The graphs y = abx and y = a (1/b) x are reflections across the x-axis.
F. Graph y = -½ (3)x and give the information on the right.
x
-2
y
Domain: _____________
Range: _______________
-1
y-intercept: ____________
0
1
Equation of Asymptote: ________
2
End Behavior:
G. Graph y = (½)x – 3 and give the information on the right.
Domain: _____________
x
-2
-1
0
1
2
y
Range: _______________
y-intercept: ____________
Equation of Asymptote: ________
End Behavior:
H. Exponential ___________ graphs approach the asymptote as x approaches negative infinity.
Exponential ___________ graphs approach the asymptote as x approaches positive infinity.
I. Describe the transformations associated with a, c and d in y = a(b)x-c + d
a>0:
a < 0:
c > 0:
c < 0:
d > 0:
d < 0:
J. Write an exponential function whose graph passes through the points (0, 8) and (3, 1).
* Does this function represent growth or decay?
K. Property of Equality for Exponential Functions: a x  a y if and only if x  y.
L. Solve:
1) 4
x
 16
5
2) 9
x 5
 1 
 
 27 
x2
3) 73 x  49 x
2
II. Logarithmic Functions:
A. The inverse of y = bx is ___________________
B. The logarithm with base 10 is called the ______________ ___________.
C. A logarithm is an operation on a number, and that number is called the _________________
of the log. The answer to a logarithm is an _______________________.
D. Inverse Properties and Special Cases: simplify or evaluate
1) logb 1 
2) log b b 
3) logb b x 
5) log 2 32 x 
6) 8log8 x =
7) log2 81 =
4) blogb x 
8) 4 log 100 =
E. Solve for x:
1) log x 125 
3
4
2) log 2
3
9
x
4
3) log 1 x  2
3
F. Property of Equality for Logarithmic Functions: logb x  logb y if and only if x  y
G. When solving logarithmic equations, always check your final answer to make sure the
argument is _____________________________.
H. Properties of Logarithms
1. State the Product Property:
2. State the Quotient Property:
3. State the Power Property:
I. Solve the following equations.
1) log3 x  log3 ( x  6)  log3 54  log3 2
2) 2log 2 x  log 2 4  3
V. Natural Logs and Solving Logarithmic Equations
A. e is an ________________ number with a value of approximately _____________________.
B. A logarithm with a base of e is called a ___________ ____________ and is written as _____.
C. Give the Change of Base Formula:______________________________________
D. To solve exponential equations where we can not make the bases match, we can __________
______________________________________ of both sides.
E. Simplify or evaluate:
1) ln e2
2) eln 0
3) ln e4  ln e3
F. Solve:
2
1) 5x 3  72
2) 4e 2 x  3  13
3) 42 x  9 x1
4) ln( x  3)  5
5) ln x  ln3x  12
6) 9  e2 x 1  10
4) e 6 ln x