# Study Guide for Math 120 Midterm One

The midterm is 85 minutes long and will be given on Wednesday, February 25, 2008 at the beginning of class. Please arrive early so that we can start on time. The test will cover chapters 3, 8, and sections 10.1 - 10.3 of the text. To study for this test, go through your homework, class handouts, and class examples. You will be allowed to use your calculator for the test . You may not share calculators or use mine. Please seek help in the Math Lab and Learning Center early and frequently.

Be familiar with the instructions specified in the textbook exercises. The wording on the test will be similar. It is important to not just know how to do a problem, but to understand what exactly the problem is asking you to do.

**Any use of other electronic devices such as cell phones
and mp3 players will result in a 0 on the exam.**

The problems shown are only examples – refer to your text
for additional problems to work on.

• Know how to use function notation and write your answers as ordered pairs .

1. Find f(3) when f(x) = 3x^{2} – 8x + 9. Write your answer as an ordered
pair.

2. Find f(−3) when f(x) = 2x^{2} +9x −4. Write your answer as an ordered pair.

• Identify the domain and range of a relation or function and write your answer
in set-builder notation.

3. Find the domain and range of the relation {(9,3),(5,3),(4,2),(−8,1)}. Write
your answer in set-builder notation.

4. Find the domain and range for the function f(x) = 3x – 7. Write your
answer in set-builder notation.

5. Find the domain and range of the function graphed to the right. Write your
answer in set-builder notation.

• Given a word problem, be able to clearly define your variables, extract the
facts, make predictions , and interpret the meanings of the slope and different
ordered pairs in the context of the problem.

6. The number of people employed in the United States as systems analysts was
431 thousand in 2000. By the year 2010, this number is expected to rise to 689
thousand. Let y be the number of systems analysts (in thousands) employed in the
United States in the year x, where x = 0 represents 2000.

Remember to clearly define your variables!

a) Write a linear function that models the number of people (in thousands)
employed as systems analysts

b) Use this function to estimate the number of people who will be employed as
systems analysts in the year 2008.

• Recognize linear and non -linear functions and graph them.

8. Use the given graph to answer the questions

a) Find f(−1). Write your answer as an ordered pair.

b) Find all x-values such that f(x) = 5

9. Graph each function.

a) f(x) = x^{2} + 3

b) h(x) = |x| − 5

c) k(x) = (x – 4)^{2}+ 1

• Algebra of functions: sum , difference, product, and quotient of functions as
well as composite functions. Also, given a function, be able to determine two
functions whose composition results in that function.

10. Use the given functions to answer the questions that follow

f(x) = x^{2} – 2 and g(x) = 3x + 1

a) Find (f + g)(x)

b) Find (f – g)(x)

c) Find (f ∙ g)(x)

d) Find (f/g) (x)

e) Find (f ° g)(x)

11. Use the given functions to answer the questions that follow. f(x) =
2x − 3, g(x) = x + 5, and h(x) = |x|

a) Write the function G(x) = 2x + 7 as a composition of f, g, or h.

12. Find f(x) and g(x) so that the given function h (x) =(f ° g)(x)

a) h(x) = (x + 3)^{2}

b) h(x)= (3x + 4)^{2} + 3

13. Given the values below, find each function value.

• Direct and inverse variation problems (8.4).

14. At sea, the distance to the horizon is directly proportional to the square
root of the elevation of the observer. If a person who is 36 feet above the
water can see 7.4 miles, find how far a person 64 feet above the water can see.
Round your answer to one decimal place.

a) Underline the sentence that you will be translating & identify the type of
variation.

b) Clearly define your variables.

c) Solve for k and give the general formula .

d) Solve the problem. Show your work and write your answer in a complete
sentence.

• Radicals and rational exponents

15. Use the properties of exponents to simplify the expression. Write with
positive exponents.

16. Use radical notation to write the expression. Then simplify your answer .

17. Multiply

18. Factor the common factor from the given expression

19. Use rational exponents to simplify each radical. Assume that all variables
represent positive numbers.

20. Use rational expressions to write as a single radical expression.

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