MATH 107 QUIZ 3
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math_107_quiz_3_problem.docxMATH 107 QUIZ 3
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(a)
Symmetric with respect to the
x-axis? _ __
y-axis? _ _
origin? _ _
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(b)
Symmetric with respect to the
x-axis? _ __
y-axis? _ __
origin? _ _ |
2. (6 pts) Let . (no explanation required)
(a) State the zero(s) of the function. ___
(b) Which of the following is true? 2. _ __
A. f is an even function.
B. f is an odd function.
C. f is both even and odd.
D. f is neither even nor odd.
3. (6 pts) Which of the following equations does the graph represent? Show work or explanation. 3. _ __
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A.
B.
C.
D.
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4. (12 pts) Consider the points(– 4, –1) and (8, 8).
(a) Find the slope-intercept equation of the line passing through the two given points. Show work.
(b) Graph the line you found in (a), eitherdrawing it on the grid in the previous problem #3, or generating the graph electronically and attaching it.
(c) Compare your line for this problem, #4, with the line in the previous 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 guestsg in a water parkthours after 9 am is given by g(t) = –32t2+224t + 263 for 0 t8.(t = 0 corresponds to 9 am)
Find andinterpretthe average rate of change of gover the interval {t | 0 t 3}= [0, 3].
Show work.
6. (20 pts) Ted's car has broken down and he needs it towed. A quick search reveals that two towing services offer the following arrangements:
Acme Towing: Pay a fee of $60.00, plus $2.50 per mile towed
or BeQuick: Pay a fee of $33.00, plus $4.00 per mile towed
(a) State a linear function f (x) that represents Acme Towing's total charge for towing a vehiclexmiles.
(b) State a linear function g(x) that represents BeQuick Towing's total charge for towing a vehiclexmiles.
(c) Ted needs to have his car towed 22 miles, as cheaply as possible. Which towing service should he choose? Show work/explanation.
(d) For what distance towed is the total towing charge exactly the same for both towing services? Show algebraic work/explanation.
(e) Fill in the blanks:
The BeQuick towing service is the cheaper option if the vehicle is towed _____( than______ miles.
A graph of y = f(x) follows. No formula for f is given. 7. __ __
Which graph (A, B, C, or D) represents the graph of y = f(x+1) 2 ?
EXPLAIN YOUR CHOICE. (Grid supplied for scratch work; You are NOT required to submit your own graph)
y = f (x)
( 2 4 -4 -2 -4 2 4 - 2 ) ( 2 4 -4 -2 -4 2 4 - 2 )
GRAPH A (below) GRAPH B(below)
( 2 4 -4 -2 -4 2 4 - 2 ) ( 2 4 -4 -2 -4 2 4 - 2 )
GRAPH C(below) GRAPH D(below)
( 2 4 -4 -2 -4 2 4 - 2 ) ( 2 4 -4 -2 -4 2 4 - 2 )
8. (20 pts, no explanation required)
Consider the graph of the piecewise function y = f (x) pictured below.
(a) State the value of f (2).
(b) State the x-intercept(s), if any.
(c) State the y-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 x-values is the function increasing?
(g) State the interval(s) on which the function is decreasing. That is, for what x-values is the function decreasing?
9. (14 ptsLife 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.
The regression line is y = 0.151x – 222.26, where x = birth year and y = U.S. female life expectancy, in years. The value of r2 is 0.9366.
(a) Use the regression line to estimate the U.S. life expectancy of a female baby born in 1970, to the nearest tenth of a year. Show some work.
(b) Use the regression line to estimate the U.S. life expectancy of a female baby born in 2016, to the nearest tenth of a year. Show some 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, r ? Also, interpret its value: Looking at the graph and the size of r, do you judge the strength of the linear relationship to be very strong, moderately strong, somewhat weak, or very weak?
U.S. Female Life Expectancy at Birth
1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 73.099999999999994 73.599999999999994 73.5 73.400000000000006 73.7 73.8 73.900000000000006 74.3 74.099999999999994 74.400000000000006 74.7 75 75.099999999999994 75.3 75.900000000000006 76.599999999999994 76.8 77.2 77.3 77.8 77.5 77.900000000000006 78.099999999999994 78.099999999999994 78.2 78.2 78.2 78.3 78.3 78.5 78.8 78.900000000000006 79.11999999999999 78.8 78.959999999999994 78.900000000000006 79.08 79.400000000000006 79.5 79.400000000000006 79.3 79.400000000000006 79.5 79.599999999999994 79.900000000000006 79.900000000000006 80.2 80.400000000000006 80.5 80.599999999999994 81 81.099999999999994
Birth Year
Life Expectancy (in years)
Y = (3/4)x + 2 -4 8 -1 8
