1. (10 pts) Consider the two graphs below. Answer the three Yes/No questions for each graph regarding symmetry. (No work required)
2. (5 pts) The amount of gas g in gallons in a car’s gas tank t days after a fill-up is modeled by
(a) (2 pts) Find and interpret g(0). Show Work.
(b) (3 pts) Find and interpret the average rate of change over the interval [0, 6]. Show work.
3. (10 pts) Answer the following questions using the graph below.
4. (10 pts) Let
(a) (3 pts) Find the zero(s) of f(x). Show Work.
(b) (7 pts) Analytically determine if f(x) is even, odd, both an even and odd, or neither. Show Work.
5. (15 pts) Consider the points (-2, 3) and (-4, -1).
(a) (5 pts) Find the point-slope equation of the line passing through the two given points. Show work.
(b) (5 pts) Graph the line from part (a) assuming the domain is (-∞, ∞). Label any x intercepts and y intercepts.
(c) (5 pts) Find the slope-intercept equation of the line containing the point (1, -1) that is also perpendicular to the line found in part (a). (The term perpendicular is discussed on page 167.) Show Work.
6. (15 pts) ABCU wants to purchase custom-made bumper stickers to advertise their university. Two websites (Website A and Website B) offer different deals:
(a) (2 pts) State a linear function f(x) that represents Website A’s total charge for an order of x bumper stickers. (No work required)
(b) (2 pts) State a linear function g(x) that represents Website B’s total charge for an order of x bumper stickers. (No work required)
(c) (3 pts) ABCU wants to purchase 250 custom-made bumper stickers as cheaply as possible. Which website should they use? Show work.
(d) (3 pts) ABCU wants to purchase 100 custom-made bumper stickers as cheaply as possible. Which website should they use? Show work.
(e) (5 pts) For what number of bumper stickers is the total charge exactly the same at both websites? Show work.
7. (5 pts) For the graph of y = f(x) shown below, select which graph represents the graph of y = f(x – 1) + 2 and explain your choice. No equation for f(x) is given.
8. (15 pts) Consider the graph of the piecewise function y = f(x) shown below.
(a) (7 pts) Determine the equation f(x) for the piecewise function shown above. See Section 1.6 #13-20 on pg 107 for examples. Show Work.
(b) (2 pts) State the range of the piecewise function. (No work required)
(c) (3 pts) State the interval(s) on which the function is increasing. That is, for what x-values is the function increasing? (No work required)
(d) State the interval(s) on which the function is decreasing. That is, for that x-values is the function decreasing? (No work required)
9. (15 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 has been prepared.
(a) (3 pts) Use the regression line to predict the U.S. life expectancy of a baby born in 2016, to the nearest tenth of a year. Show work
(b) (4 pts) Use the regression line to predict the birth year in which the U.S. life expectancy will hit 80 years, rounding up to the nearest whole year. Show work.
(c) (4 pts) State the slope of the regression line, its units of measurement, and interpret the meaning of the slope. (No work required)
(d) (4 pts) Calculate the value of the correlation coefficient, R. Based on the correlation coefficient, is the strength of the linear relationship strong, moderate, or weak? Show work.