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Math 112 – College Algebra I
EXAM THREE: Sections 2.5, R.3, R.5, R.6, R.
Tuesday, March 31, 2009
Name: Answer Key
Instructor: ClassTime/Section:
- Show all work to receive credit for each of the problems.
- Incorrect answers with incorrect work shown or no work shown will NOT receive any credit.
- Circle your answers and when appropriate label them.
- Give answers to written questions in complete sentences.
- (4 pts) Solve the following equation for symbolically for x. € x − 5 − 2 = 4 € x − 5 = 6 x − 5 = 6 or x − 5 = − 6 x = 11 or x = − 1
- (4 pts) Solve the inequality symbolically for x. Write the solution set in interval notation. € 3 − 4 x > 5 € 3 − 4 x > 5 or 3 − 4 x < − 5 − 4 x > 2 or − 4 x < − 8 x < −
or x > 2 −∞,− 1
- (3 pts) The graphs of two functions f and g are shown in the figure at the right. Solve the inequality € f (^) ( x ) ≥ g (^) ( x ). Give answer in interval notation.
[^ − 2 ,^4 ]
f ( x )
g ( x )
- (4 pts) The table below shows the temperature at three times during the day on March 9, 2009. Assume that the temperature rose and fell at a constant rate. Time (hours past midnight) 9 17 23 Temperature in degrees Fahrenheit 35.3 46.0 37. Find the values for the constants a, b and c symbolically, so that € T (^) ( x ) models the data exactly. Let x be the hours past midnight. You must show your work to get credit for the problem. € T (^) ( x ) = 1.3375( x − (^9) ) + 35.3 if 9 ≤ x < 17 a (^) ( x − b ) + c if 17 ≤ x ≤ 23
a =
a = −1. b = 23 c = 37. or € a = −1. b = 17 c = 46
- Use € f (^) ( x ) to complete the following. € f (^) ( x ) = 2 x + 5 if - 5 ≤ x ≤ - 2 if - 3 < x ≤ 4
a. (2 pts) Give the domain of € f (^) ( x ) € [^ − 5 ,^4 ] b. (4 pts) Evaluate each of the following. € f (^) (− 3 ) = - 1 € f (^) ( 2 ) = 2 c. (5 pts) Sketch the graph of f (^) ( x ).
- (3 pts each) Simplify the expressions. Assume that all variables are positive. Write answers in exponential notational without negative exponents. a. € x^3 y
4 x^12 y −^4 b. € − 2 −^3 x^2 xy −^3
− 2 € x 12 y 4 x 12 y − 4 = y^8 € xy 3 − 2 3
− 2
x − 2 y − 6 2 − 6
x 2 y 6 a. € y^6 x^4 b. € x (^3 ) ⋅ x 5 € y 3 x 2 € x (^53) ⋅ x (^52) = x (^256) c. € x
1 5 x^2
2 3 d. € p^1 4 p^3 /^4 + p^1
x − (^35) x
43 =^
x (^2915) € p + p (^12)
- (4 pts each) Factor each polynomial completely. a. € 10 x^3 + 3 x^2 − x b. € 16 x^2 y + 2 xy + 4 y € x 10 x^2 + 3 x − 1
x 10 x 2
x (^) [ 5 x (^) ( 2 x + (^1) ) − (^1) ( 2 x + (^1) )] x (^) ( 2 x + (^1) ) ( 5 x − (^1) ) € 2 y 8 x^2 + x + 2
c. € 2 x 3
- 3 x 2
- 2 x + 3 d. € 4 x 2 − 36 x + 81 € x 2 (^2 x^ +^3 ) +^1 (^2 x^ +^3 ) (^2 x^ +^3 ) x^2 +^1
(^2 x^ −^9 ) (^2 x^ −^9 ) =^ (^2 x^ −^9 ) 2
- (4 pts each) Simplify the following expressions. a. € x^2 − 7 x + 6 x^2 − 2 x − 15
x − 9 x^2 − 2 x − 15 b. €
x + 3
5 x + 1 x^2 + 9 x + 18 x^2 − 7 x + 6 − x + 9 x 2 − 2 x − 15 x^2 − 8 x + 15 (^ x^ −^5 ) ( x^ +^3 ) (^ x^ −^5 )( x^ −^3 ) (^ x^ −^5 ) ( x^ +^3 ) x − 3 x + 3 € (^2) ( x + (^6) ) (^ x^ +^3 ) ( x^ +^6 )
5 x + 1 (^ x^ +^3 ) ( x^ +^6 ) 2 x + 12 + 5 x + 1 (^ x^ +^3 ) ( x^ +^6 ) 7 x + 13 (^ x^ +^3 ) ( x^ +^6 )
