1. Graph the exponential function by hand. Identify any asymptotes and intercepts and determine whether the graph of the function is increasing or decreasing. (Enter NONE in any unused answer blanks.)
$ f(x) = \left(\dfrac{{\color{red}11}}{{\color{red}10}}\right)^x $
Equation of horizontal asymptote:
Equation of vertical asymptote:
Value of y-intercept
Value of x-intercept
The function is
2. Use the graph of y = 2x to match the function with its graph.
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Maple Generated Plot
A
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Maple Generated Plot
B
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Maple Generated Plot
C
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Maple Generated Plot
D
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y = 2x – 4
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y = 2x – 5
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y = 2x + 4
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y = 2–x
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3. Use the graph of f to describe the transformation that yields the graph of g. Then sketch the graphs of f and g by hand.
f(x) = −2x, g(x) = 5 − 2x
The graph of g(x) = 5 − 2x is a vertical shift five units downward of f(x) = −2x.
The graph of g(x) = 5 − 2x is a horizontal shift five units to the left of f(x) = −2x.
The graph of g(x) = 5 − 2x is a vertical shift five units upward of f(x) = −2x.
The graph of g(x) = 5 − 2x is a horizontal shift five units to the right of f(x) = −2x.
Sketch the graphs of f and g.
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WebAssign Plot
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WebAssign Plot
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WebAssign Plot
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WebAssign Plot
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4. Use a graphing utility to construct a table of values for the function. (Round your answers to three decimal places.)
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x
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f(x) = 5x − 3
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-1
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0
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1
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2
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3
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Sketch the graph of the function.
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WebAssign Plot
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WebAssign Plot
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WebAssign Plot
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WebAssign Plot
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Identify any asymptotes of the graph. (Enter NONE in any unused answer blanks.)
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vertical asymptote
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x
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=
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horizontal asymptote
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y
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=
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5. Use a graphing utility to construct a table of values for the function. (Round your answers to three decimal places.)
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x
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g(x) = 4 − e−3x
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-4
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-3
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-2
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-1
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0
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Sketch the graph of the function.
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WebAssign Plot
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WebAssign Plot
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WebAssign Plot
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WebAssign Plot
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Identify any asymptotes of the graph. (Enter NONE in any unused answer blanks.)
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vertical asymptote
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x
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=
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horizontal asymptote
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y
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=
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6. Fill in the blank.
If
x = ey,
then y = .
7. For what value of x is
ln x = ln 9?
x =
8. Write the logarithmic equation in exponential form. For example, the exponential form of
log5 25 = 2 is 52 = 25.
log2 512 = 9
9. Write the logarithmic equation in exponential form. For example, the exponential form of log5 25 = 2 is 52 = 25.
log
= -8
10. Write the exponential equation in logarithmic form. For example, the logarithmic form of
23 = 8 is log2(8) = 3.
43/2 = 8
log
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http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/leftparen1.gif
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http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/rightparen1.gif
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=
11. Use a calculator to evaluate the function at the indicated value of x. Round your result to three decimal places.
f(x) = log10(x) x = 4/5
12. Solve the equation for x.
log10(102) = x
13. Write the logarithmic equation in exponential form. For example, the exponential form of ln(5) = 1.6094... is e1.6094... = 5. (Do not use ... in your answer.)
$ \ln ({\color{red}2}) = {\color{red}0.6931} \dots $
14. Write the exponential equation in logarithmic form. For example, the logarithmic form of
e2 = 7.3890 http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/ldots.gif
is ln 7.3890 http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/ldots.gif
= 2.
(Do not use ... in your answer.)
e2.2 = 9.0250 http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/ldots.gif
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ln
=
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15. Use the properties of natural logarithms to rewrite the expression.
5 ln(e5)
16. Use the properties of logarithms to rewrite and simplify the logarithmic expression.
ln
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http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/leftparen1.gif
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http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/rightparen1.gif
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17. Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
log9(9x)
18. Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
ln
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http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/leftparen1.gif
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7
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http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/sqrt1a.gif
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t
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http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/rightparen1.gif
19. Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
ln
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http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/leftparen3.gif
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http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/sqrt5a.gif
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http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/rightparen3.gif
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20. Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
ln
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http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/leftparen2.gif
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http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/rightparen2.gif
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, x > 2
21. Condense the expression to the logarithm of a single quantity.
5 ln x + 2 ln y − 3 ln z
22. Use a graphing utility to graph the function and approximate its zero accurate to three decimal places.
h(t) = e0.125t − 3
t =
23. Solve the logarithmic equation algebraically. Round the result to three decimal places. Verify your answer using a graphing utility. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
ln 9x = 1.6
x =
24. Use the zero or root feature of a graphing utility to approximate the solution of the logarithmic equation. (Enter your answers as a comma-separated list. Round your answers to three decimal places.)
ln x + ln(x2 + 4) = 11
x =
25. Use a graphing utility to approximate the point of intersection of the graphs. Round your result to three decimal places.
y1 = 1.03
y2 = ln
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http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/sqrt1a.gif
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x − 4
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(x, y) =
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http://www.webassign.net/wastatic/wacachea0a080f42e6f13b3a2df133f073095dd/watex/img/leftparen1.gif
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