Algebra 2 Ch6 REVIEW - SHOW ALL WORK FOR FULL CREDIT Name: ______
Multiple Choice
Simplify the expression.
____1.
a. / / c. /b. / / d. /
____2.
a. / / c. /b. / / d. /
____3.
a. / / c. /b. / / d. /
____4.The height H (in centimeters) of a container being printed by a 3-D printer is related to the radial position r (in centimeters) by the equation . Describe the transformation of represented by H. Then use the function to determine the height of the container when the radial position is 1.1centimeters.
a. / The graph of H is a vertical shrink by a factor of 2.9 followed by a translation 2.6centimeters down of the graph of f ; about 4.6cmb. / The graph of H is a translation 2.6centimeters down followed by a vertical stretch by a factor of 2.9 of the graph of f ; about 4.6cm
c. / The graph of H is a translation 2.6centimeters down followed by vertical shrink by a factor of 2.9 of the graph of f ; about 4.6cm
d. / The graph of H is a vertical stretch by a factor of 2.9 followed by a translation 2.6centimeters down of the graph of f ; about 4.6cm
____5.Your friend deposits $5000 in an investment account that earns 3.4% annual interest. Find the balance after 12 years when the interest is compounded daily.
a. / $7519.04 / c. / $7518.89b. / $7514.70 / d. / $7468.21
Rewrite the equation in logarithmic form.
____6.
a. / / c. /b. / / d. /
____7.
a. / / c. /b. / / d. /
Evaluate the logarithm.
____8.
a. / 0.001 / c. /b. / 3 / d. / –3
____9.
a. / / c. /b. / / d. /
____10.Simplify .
a. / / c. / 4b. / 1 / d. / 6
Find the inverse of the function. SHOW WORK.
____11.
a. / / c. /b. / / d. /
____12.
a. / / c. /b. / / d. /
Write a rule for g that represents the indicated transformations of the graph of f.
____13.; translation 7 units left followed by a horizontal shrink by a factor of
a. / / c. /b. / / d. /
Expand the logarithmic expression.
____14.
a. / / c. /b. / / d. /
____15.
a. / / c. /b. / / d. /
Condense the logarithmic expression.
____16.
a. / / c. /b. / / d. /
____17.Evaluate .
a. / 4.344 / c. / 3.133b. / 2.489 / d. / 1.886
Solve the equation. SHOW ALL WORK and CHECK FOR EXTRANEOUS SOLUTIONS.
____18.
a. / / c. /b. / / d. /
____19.
a. / x = 15 / c. / x = 1b. / x = 5 / d. / x = 3
____20.
a. / x = 7 / c. / x = 76b. / x = 86 / d. / x = 59
____21.
a. / / c. / andb. / / d. /
Solve the inequality. SHOW ALL WORK
____22.
a. / / c. /b. / / d. /
____23.Write an exponential function whose graph passes through (1, 6) and (3, 54).
a. / / c. /b. / / d. /
Tell whether the function represents exponential growth or exponential decay and explain why. Then graph the function in problem 24.
24. ______; ______
25. ______; ______
26. y = e-5x ______; ______
Describe the transformation of f represented by g.
27.f(x) = 3x; g(x) = 3x-2 ______
28.; ______; ______
29. Determine the type of function represented by the table. Explain and show work for your reasoning
x / –1 / 1 / 3 / 5 / 7y / 7 / 35 / 175 / 875 / 4375
30.A park ranger is studying the population of a bird species that nests within the park boundaries. The table shows the numbers y of birds nesting during the xth year since the study began. Use your calculator to find an exponential function that models the data.______
Then use your equation to find the number of birds in the 8th year: ______
Year,x / Number of birds, y1 / 8
2 / 11
3 / 15
4 / 21
5 / 29
31.The value of a home ycan be approximated by the model y = 134,000(1.05)t where t is the number of years since 2010.
a. Tell whether the model represents exponential growth or exponential decay.
b. Identify the annual percent increase or decrease in the value of the home.
c. Find the year when the value of the home will be $293,000. SHOW ALL WORK