Math 107 quiz 3 | Mathematics homework help

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)

q3Wgraph.gif

 

Symmetric with respect to the

 

x-axis? _ __

 

y-axis? _ _

 

origin? _ _

 

(b)

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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. 

 

 

 

 

q3LineOL1.gif

 

 

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.

 

q3piecewise.gif

 

(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?