## [answered] MATH 107 Quiz 3 Name: _____________________________________

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MATH 107 Quiz 3

Name: ______________________________________________

I have completed this assignment by myself, working independently and not consulting anyone, except

the instructor. The answer to the following questions are worth the points indicated for a total

of 100 points possible.

1. (6 pts) For each graph, is the graph symmetric with respect to the -axis, -axis, and origin? No

explanation required. Just answer Yes or No to each question. Symmetric with respect to the Symmetric with respect to the -axis: _____ -axis: _____ -axis: _____ -axis: _____ origin: _____ origin: _____ 2. (6 pts) Let ( ) = | | ? 4. No explanation required.

a. State the zero(s) of the function. b. Which of the following is true?

A.

B.

C.

D. is an even function.

is an odd function.

is both even and odd.

is neither even nor odd. 3. (6 pts) Which of the following equations does the graph represent? Show work or explanation. A. = +5 B. = +8 C. = +7 D. = ?5 4. (12 pts) Consider the points (?2,5) and (6,0).

a. Find the slope-intercept equation of the line passing through the two given points.

Show work. b. Graph the line, either drawing it on the grid below, or generating the graph

electronically and attaching it. c. Compare your line for problem #4 with the line in problem #3. Are the two lines

parallel, perpendicular, or neither parallel nor perpendicular? The terms parallel and

perpendicular are discussed on pages 166 and 167. No explanation required ? just

state the answer. 5. (8 pts) The number of guests

( ) =? in a water park hours after 10 am is given by: + 35 + 165 for 0 ? ? 8 Find and interpret the average rate of change of

Show work. ( = 0 corresponds to 10 am) over the interval { | 2 ? ? 7} = [2, 7]. 6. (20 pts) Patti wants to purchase custom-made shirts to advertise her business. Two companies

offer different deals:

Company A: Pay a design fee of \$40.00, plus \$10.50 per shirt

Company B: Pay a design fee of \$65.00, plus \$7.00 per shirt

a. State a linear function ( ) that represents Company A's total charge for an order of

shirts.

b. State a linear function ( ) that represents Company B's total charge for an order of

shirts.

c. Patti wants to purchase 140 custom-made shirts, as cheaply as possible. With which

company should she place her order? Show work. d. For what number of shirts is the total charge exactly the same for both companies?

Show work. e. Fill in the blanks: Company A is the cheaper option if ________ (less or more) than

_______ (enter number) shirts are ordered. 7. (8 pts) Below is a graph of = ( ) follows. No formula for is given. Which graph (A, B, C, or D) represents the graph of = ( + 2) + 3? Explain your choice. A

blank grid is supplied for scratch work; You are NOT required to submit your own graph. A B C D 8. (20 pts) Consider the graph of the piecewise function

explanation required. = ( ) pictured below. No a. State the value of (? ). b. State the -intercept(s), if any. c. State the -intercept(s), if any. d. State the domain of the piecewise function. e. State the range of the piecewise function. f. State the interval(s) on which the function is increasing. That is, for what -values is the

function increasing? g. State the interval(s) on which the function is decreasing. That is, for what -values is the

function decreasing? 9. (14 pts) Life expectancy at birth is the estimated lifespan of a baby born in a particular year

(given the conditions of that time period). Based on data retrieved from

http://www.indexmundi.com/facts/united-states/life-expectancy-at-birth the following chart of

U.S. life expectancy for females has been prepared. Life Expectancy (in years) U.S. Female Life Expectancy at Birth

83

82

81

80

79

78

77

76

75

74

73

72

1950 y = 0.1498x - 219.97

R? = 0.95 1960 1970 1980 1990 2000 2010 2020 Birth Year The regression line is = 0.1498 ? 219.97, where

expectancy, in years. The value of is 0.95. = birth year and = U.S. female life a. Use the regression line to estimate the U.S. life expectancy of a female baby born in

1980, to the nearest tenth of a year. Show work. b. Use the regression line to predict the U.S. life expectancy of a female baby born in 2020,

to the nearest tenth of a year. Show work. c. What is the slope of the regression line and what are the units of measurement? In a

sentence, interpret what the slope is telling us, in the context of this real-world

application. d. What is the value of the correlation coefficient, ? Also, interpret its value. Looking at

the graph and the size of , do you judge the strength of the linear relationship to be

very strong, moderately strong, somewhat weak, or very weak?

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