Statistics

Question description

(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.)

2. (6 pts) Let =−8. (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.

(a)

Symmetric with respect to the
x-axis? ____
y-axis? ____
origin? ____

(b)

Symmetric with respect to the
x-axis? ____
y-axis? ____
origin? ____
3. (6 pts) Which of the following equations does the graph represent? Show work or explanation. 3. ______

A. =−! !+8
B. =−! !+6
C. =! !+6
D. =! !+6

4. (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), either drawing 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 guests g in a water park t hours after 9 am is given

by g(t) = –32t2 + 222t + 272 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.

6. (20 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 mug or Company B: Pay a design fee of $108.00, plus $3.75 per mug

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

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

(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: Company A is the cheaper option if ________(choose

less or more) than ______ (enter number) mugs are ordered.

7.

(8 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)

2 4 4 -2 -4
2 4
-2 2 4 4 4 22 44
2 4
2
2 4 4 -2 -4
2 4
-2 2 4 -4 -2 -4
2 4
-2
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 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… 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?