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Simplify. Assume that no denominator is equal to zero.
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1.
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2.
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3.
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4.
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Rewrite the equation in exponential form.
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5.
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Expand the logarithmic expression.
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6.
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7.
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8.
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After a certain drug is injected into a patient, the concentration C of
the drug in the bloodstream is monitored. At time t > 0 (in minutes since the injection), the
concentration (in mg/L) is given by  . What is the eventual
concentration of the drug? a. | 0 mg/L | b. | 10 mg/L | c. | 2
mg/L |
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9.
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Find the intercepts and asymptotes of the rational function  . a. | x–intercept y–intercept horizontal
asymptote vertical asymptote
( 24, 0 )
( 0, 2 ) y =
0
x = 3 | b. | x–intercept y–intercept horizontal
asymptote vertical asymptote
( –8, 0 )
( 0, 6 ) y =
–1.5
x = 2 | c. | x–intercept y–intercept horizontal
asymptote vertical asymptote
( 3, 0
) ( 0, 24
) y =
0
x = 24 |
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Describe the transformation of f represented by g. Then graph
each function.
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10.
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 ; 
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11.
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 ; 
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12.
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 ; 
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13.
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Find the intercepts and asymptotes of the rational function  . a. | x–intercept y–intercept horizontal
asymptote vertical asymptote
( 6, 0 )
( 0, 3 ) y
= 1
x = 2 | b. | x–intercept y–intercept horizontal
asymptote vertical asymptote
( 2, 0 )
( 0, 3 ) y
= 0
x = 6 | c. | x–intercept y–intercept horizontal
asymptote vertical asymptote
( 6, 0 )
( 0, 2 ) y
= 0
x = 2 |
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Factor the trinomial, if possible. If the trinomial cannot be factored using
integers, write prime.
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14.
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15.
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16.
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17.
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Graph  .
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18.
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Find the horizontal and vertical asymptotes of the rational function  . a. | horizontal asymptote y = 3; vertical asymptote x =
–6 | b. | horizontal asymptote y = 3; vertical asymptote x =
6 | c. | horizontal asymptote y = 0; vertical asymptote x =
–6 |
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Factor the trinomial.
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19.
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20.
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21.
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22.
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The graph of g is a transformation of the graph of f. Write a
rule for g.
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23.
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24.
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Rewrite the equation in logarithmic form.
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25.
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26.
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Condense the logarithmic expression.
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27.
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28.
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Tell whether the function represents exponential growth or
exponential decay. Explain your reasoning.
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29.
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30.
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Find the inverse of the function.
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31.
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Factor the polynomial.
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32.
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33.
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Simplify the expression.
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34.
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35.
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36.
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37.
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Find the x– and y–intercepts of the rational
function  . a. | x–intercept ( 8, 0 ), y–intercept ( –1, 0
) | b. | x–intercept ( –1, 0 ), y–intercept ( 1, 0
) | c. | x–intercept ( –1, 0 ), y–intercept ( 8, 0
) |
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Evaluate the logarithm.
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38.
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Simplify the given expression. Assume that no variable equals 0.
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39.
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40.
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Find the x– and y–intercepts of the rational
function  . a. | x–intercept ( –6, 0 ), y–intercept ( 216, 0
) | b. | x–intercept ( 216, 0 ), y–intercept ( –216, 0
) | c. | x–intercept ( 6, 0 ), y–intercept ( –216, 0
) |
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41.
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Find the vertical asymptote of the rational function  .
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42.
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The rabbit population on Mr. Jenkins' farm follows the formula  where t > 0 is the time in months since the beginning of the year. What is the
eventual population of rabbits?
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Solve the equation.
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43.
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a. | x = 26 | c. | x = 631 | b. | x = 619 | d. | x = 1030 |
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Simplify the given expression.
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44.
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Graph the equation.
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45.
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46.
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