finite math

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NAME ____________________________________

MATH 115 - FINITE MATH

INSTRUCTOR: CYNTHIA COUNTER

MIDTERM

(26 problems worth a total of 100 points)

{ }0,1, 2, 3, 4, 5, 6, 7,8, 9U =

{ }0, 2, 4, 6A =

{ }1, 2, 3, 4B =

1. Find A B∪ . (4 points)

2. Find A B∩ . (4 points)

3. Find B A− . (4 points)

4. Find A′ . (4 points)

5. Is { }1, 2, 3 B⊆ ? Explain briefly. (4 points)

Consider the function defined below.

( )4 16f − = − ( )3 12f − = − ( )2 8f − = − ( )1 4f − = − ( )0 0f =

( )1 4f = ( )2 8f = ( )3 12f = ( )4 16f =

6. Write the domain as a set. (2 points)

7. Write the range as a set. (2 points)

8. What type of sequence does the range form? (2 points)

9. Write an equation in function notation that represents this sequence. (4 points)

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10. Write f as a set of ordered pairs. (2 points)

11. Graph f. (4 points)

Define a function f as

( )

1 3

64 f − = ( )

1 2

16 f − = ( )

1 1

4 f − = ( )0 1f =

( )1 4f = ( )2 16f = ( )3 64f =

12. Write the range as a set. (2 points)

13. What type of sequence does the range form? (2 points)

14. Write an equation in function notation that represents this sequence. (4 points)

15. Graph the function for a domain of all real numbers. (4 points)

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16. A supplier is willing to supply 100 items at $200 per item, but is willing to supply 150 items at $240 per item. Assume a linear relationship with quantity as the independent variable in

order to find the supply equation. (5 points)

17. Consumers are willing to spend $420 per item if 80 items are available, but are only willing to spend $280 per item if 160 items are available. Assume a linear relationship with quantity

as the independent variable in order to find the demand equation. (5 points)

18. Find the equilibrium point (quantity, price). Round the quantity to the nearest whole number and the price to the nearest dollar. (5 points)

19. Make a rough sketch of the supply and demand lines (the graph does not need to be to scale), and note the equilibrium point. Be sure to label each of the lines and their y-

intercepts as well as the equilibrium point. (4 points)

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20. How much money will an investor have in 15 years if she invests $20,000 at 2.1% simple interest? (5 points)

21. How much money should an investor invest now at 3.2% simple interest if he wants to have $30,000 in 5 years? (5 points)

22. How long will it take for $35,000 invested at 2.5% simple interest to grow to $50,000? (5 points)

Let ( ) 2 6f x x= − .

23. Find the x- and y-intercepts? (5 points)

Simple Interest

PrA P t= + (1 )A P rt= +

Where A = Accumulated Amount/Future Value

P = Principal/Initial Investment Amount/Present Value

r = Annual Interest Rate (as a decimal)

t = time (years)

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24. Graph f using the intercepts and then graph 1f − using the intercepts on the same graph. Be

sure to label the intercepts and identify each function. (5 points)

25. Find the equation for 1f − . (4 points)

26. Verify that the two functions are inverses by using the cancellation equations. Be sure to show the correct order of the cancellations. (4 points)