MATH_QUIZ

1. (10 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 thex-axis? ____y-axis? ____origin? ____(b)Symmetric with respect to thex-axis? ____y-axis? ____origin? ____2. (10 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. (10 pts)  Which of the following equations does the graph represent? Show work or explanation.       3. ______A.B.C.D.4. (10 pts) Look at the graph of the quadratic function and complete the table.[No explanations required.]GraphFill in the blanksEquation(a) State thevertex:____________(b) State therange:_____________(c) State the interval on which the function is increasing:_____________(d) The graph represents which of the following equations?Choice:____A.    y  =  –x2+4x– 3B.    y  =  –2×2 –x + 3C.    y  =  x2 – 2x– 3D.    y  =  x2+ 2x– 35. (10 pts) Consider the points(– 3, 7) and (3, –1).(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.6. (10 pts) The number of guests g in a water park t hours after 9 am is given by                                                     g(t) = –32t2 + 224t + 266 for  0 £t£ 8.  (t = 0 corresponds to 9 am)Find  and interpret the average rate of change of g over the interval {t | 4 £t£ 7}  = [4, 7].Show work.7. (10 pts) Luke wants to purchase custom-made mugs to advertise his business. Two companies offer different deals:Company A:  Pay a design fee of $50.00, plus $4.50 per mugor     Company B:  Pay a design fee of $92.00, plus $3.90 per mug(a) State a linear function f (x) that represents Company A’s total charge for an order of xmugs.(b) State a linear function g(x) that represents Company B’s total charge for an order of xmugs.(c) Luke wants to purchase 120 custom-made mugs, as cheaply as possible. With which company should he place his order? Show work/explanation.(d) For what number of mugs is the total charge exactly the same for both companies? Show algebraic work/explanation.(e) Fill in the blanks:CompanyA is the cheaper option if  ________(choose lessor more) than______ (enter number)mugs are ordered.8. (10 pts) 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) -1 ?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)9. (10 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?10. (10 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 males has been prepared.The regression line is y = 0.2052x  – 336.5, where x = birth year and y = U.S. life male expectancy, in years. The value of r2 is 0.9809.(a)  Use the regression line to estimate the U.S. life expectancy of a male baby born in 1970, to the nearest tenth of a year. Show some work.(b)  Use the regression line to predict the U.S. life expectancy of a male baby born in 2020, 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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