Mathematics quiz
MATH 107 QUIZ 3
1. (6 pts) For each graph, is the graph symmetric with respect to the x-axis? y-axis? origin?(No explanation required. Just answer Yes or No to each question.)
| (a)
Symmetric with respect to the
x-axis? _ __
y-axis? _ _
origin? _ _
|
(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. _ __
|
A.
B.
C.
D.
|
|
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 £t£8.(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)
GRAPH A (below) GRAPH B(below)
GRAPH C(below) GRAPH D(below)
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?
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