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Unformatted text preview: Test 3 Study Guide
(Show your work) Math 1101
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1. 1)Determine (with reason) if the function f(x):3 x2 +5 is one—to—one.
. . . . 8 .
2)Deterrn1ne (w1th reason) if the funct1on f(x)=— — IS one~to~one.
x 3)Determine (with reason) if the function f(x)= 12x~8 is one~to~one. 4) Determine whether the function f(x)=5 x2+7 is even, odd, or neither. 5) Determine whether the function f(x)=— E: is even, odd, or neither. X 6) Determine whether the function f(X)= 12x8 is even, odd, or neither. 2. Consider the function y: x2 and y: (x + 2)2 +7
21) Sketch the graph of the pair of functions. b) Describe the transformation used to obtain the graph of the second function from the ﬁrst
function. 3. Consider the function y: 5 x2 and y: 5 (x + 2)2 ~7
a) Sketch the graph of the pair of functions. b) Describe the transformation used to obtain the graph of the second function from the ﬁrst
function. 4. Consider the function y: Ix] and y=[x  4[ — 3
a) Sketch the graph of the pair of functions. b) Describe the transformation used to obtain the graph of the second function from the first
function. 5. Consider the function y: [x1 and y: 1x  4[ + 3
3) Sketch the graph of the pair of functions. b) Describe the transformation used to obtain the graph of the second function from the first
function. 6. The number of cellular subscribers, in millions, can be modeled by the function
S (x) = 0.00043x4‘157 , where X is the number of years after 1979.
a) Use the model to find the number of subscribers in 1997. b) Rewrite a new model C(x) with x equal to the number of years after 1987. c) Use the new model to find the number of subscribers in 1997. 7. Let £0025 x2— 7 and g(x)= 3x — 6, find the following
a) (f+g)(2) b) (f 9(2)
0) (f0 g)(2)
d) (fgXX) f e) (~)(x) and its domain
5’ f) (g 0 f)(X) 8. If f(x) = 5x—7 and g(x)= x27 . a) Find (f o g)(X). (simplify your answer) b) Find (g o f)(x). (simplify your answer) c) Find (f o f)(x). (simplify your answer) 9. If f(x) = 6X+1 and g(x)= 42x ~3 .
a) Find (f o g)(x). (simplify your answer) b) Find (go f)(x). (simplify your answer)
10. Let f(X) be the function y=5x—7. Find the inverse function of f(x) 11. The total revenue function for a product is given by R=520x dollars, and the total cost function for this same product is given by C=12,OOO+9OX+x2, where C is measured in dollars.
For both functions, the input X is the number of units produced and sold. a). Find the profit function for this product from the two given functions.
b). What is the profit when 132 units are produced and sold?
c). How many units must be produced and sold to maximize the profit? d). What is the maximum profit? 12. On a given day, each schilling was worth 2.57 rubles and each peso was worth 0.018
schillings. Find the value of 1000 pesos in rubles on that day. 13. Simplify the exponential expression and write your answer using only positive exponents. l) 1214f“)7 —6x"31x4 2) aob~3(c—2)‘3 (vol
5 3 3 x y ) way3f
5 5 4 U m ) mamas 14. Multiply and divide. Write the result using scientific notation 1) (5.8x106)(9.5x104) 5.8><105 2 ___
) 25x1016 15. Use properties of exponents to simplify the expression. balm who 16. At the end of an advertising campaign, weekly sales declined according to the equation
y=200900 (3 '0‘05“ ) dollars, where x is the number of weeks after the end of the campaign. a) Determine the sales at the end of the campaign.
b) Determine the sales 5 weeks after the end of the campaign. 17. The population of a city was 280000 in 1995 and its population after 1995 is given by the function P( T )2280000 e001”, where T is the number of years since 1995. Use this function to
calculate the population in 2007. 18. The population in a certain city was 800,000 in 2003, and its future size is predicted to be
p = 800,000e'0'02m people, where t is the number of years after 2003. a) Does this model indicate the population is increasing or decreasing? b) Use this function to predict the population of the city in 2010. c) Use this function to predict the population of the city in 2020. d) What is the average rate of change in population between 2010 and 2020? ...
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 Fall '08
 HARDEN
 Math, Exponentiation, Binary relation

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