College Algebra

Order instructions

  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? _______

 

 

 

 

  1. (6 pts) Let . No explanation required.

 

(a) State the zero(s) of the function:________

 

(b)  Which of the following is true?     2. ________

  1. f  is an even function.
  2. f  is an odd function.
  3. f  is both even and odd.
  4. f  is neither even nor odd.

 

  1. (6 pts) Which of the following equations does the graph represent? Show work or explanation.

 

 

 

A.

 

 

B.

 

 

C.

 

 

D.

 

 

 

 

 

 

 

  1. (12 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 below, 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?  Explain.

 

  1. (8 pts) The number of guests g in a water park t hours after 9 am is given by:

g(t) = –28t2 + 220t + 250 for  0 £t£ 8.  (t = 0 corresponds to 9 am)

Find and interpret the average rate of change of g over the interval {t | 3£t£ 7} = [3, 7].Show work.

  1. (20 pts) John wants to purchase custom-made shirts to advertise his business. Two companies offer different deals:

Company A:  Pay a design fee of $60.00, plus $6.50 per shirt

Company B:  Pay a design fee of $100.00, plus $6.00 per shirt

 

(a) State a linear function f (x) that represents Company A’s total charge for an order of xshirts.

(b) State a linear function g(x) that represents Company B’s total charge for an order of xshirts.

(c) John wants to purchase 120 custom-made shirts, as cheaply as possible. With which company should he place his order? Show work/explanation.

 

(d) For what number of shirts 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)shirts are ordered.

  1. (8 pts) A graph of y = f (x) follows. No formula for f is given.

Which graph (A, B, C, or D) represents the graph,y = f (x 2) +1?EXPLAIN YOUR CHOICE.

Grid supplied for scratch work; you are NOT required to submit your own graph.

 

                        y = f (x)                                                                              Scratch Work

 

Graph A (below)                                                          Graph B (below)

 

Graph C (below)                                                          Graph D (below)

  1. (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?

  1. (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.

 

The regression line is y = 0.1784x – 279.99, where x = birth year and y = U.S. female life expectancy, in years. The value of r2 is 0.9814.

(a)  Use the regression line to estimate the U.S. life expectancy of a female baby born in 1975, to the nearest tenth of a year. Show some 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 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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