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Pre-Calculus – Semester Exam ReviewSCORE ______

(Chapters Summer, 1-3)

Chapter 258Glencoe Precalculus

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Part 1: ACT 60 Questions: Please review your ACT notes

Part 2: Short Response
Instructions: Write your answer in the space provided.

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1. Find f ◦ g for f(x) = –4 and g(x) = .

2. Find the zeroes of the function f(x) = 2+ 3–5x –6.

3. Describe the type of discontinuity that exists at x = 5 in

h(x) =

4. Graph f(x) = –4.

5. Solve 15 –4 log 2x = –1.

6. Solve = .

7. Uranium-235 has a half-life of 704 million years. How manygrams of uranium will remain after 1 million years if youstart with a sample of 100 grams?

8. CENSUS The table gives the U.S. population in millionsbetween 1960 and 2000. Let 1960 = 0. Write an equation forthe line of best fit.

Year / 1960 / 1970 / 1980 / 1990 / 2000
Population / 179.3 / 203.2 / 226.5 / 248.7 / 281.4

Source: U.S. Census Bureau

9. Use your model from Question 26 to predict when thepopulation in the U.S.
will reach 350,000,000.

10. Given f(x) = 2 log2 (x + 4).

a. Sketch the graph.

b. Describe the domain and range of the function.

c. Describe the asymptotes and end behavior of the function.

d. State where the function is increasing or decreasing.

Part 3: Essay Response
Instructions: Write your answer in the space provided.

Please be able to answer ALL questions below. For the exam, only 3 will be picked.

1. a. Draw the parent graph and each of the three transformations that would result in the graph shown below. Write the function for each graph. Describe the transformation.

b. Determine the domain and range of the graph shown above. Use interval notation.

c. Describe the extrema and end behavior of the graph shown above.

d. For the function whose graph is shown above, find the average rate of change on the interval [1, 4].

2. Describe how to find an inverse numerically, algebraically, and graphically.

3. Use what you have learned about the zeros of a function to answer the question.

Write a polynomial function of least degree with three real zeros. Explain your answer.

4. A 36-foot-tall light pole has a 39-foot-long wire attached to its top. A stake will be driven into the ground to secure the other end of the wire. The distance from the pole to where the stake should be driven is given by the equation
39 = d2+362, where d represents the distance in feet.

a. Find d.

b. What relationship was used to write the given equation? What do the values 39, 36, and d represent?

5. Explain how to solve the equation . Algebraically and graphically.