1. 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? ____
2.Let f(x)=|x|-3. (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. Which of the following equations does the graph represent? Show work or explanation.
3. ______
A. y= 2/3 x+4
B. y= 3/2 x+4
C. y=- 3/2 x+4
D. y=- 2/3 x+4
4. Consider the points(-5, -2) and (-1, 4).
(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. The amount of home heating oil h in gallons in a tank t days after a fill-up is modeled by
h(t) = -0.08t2- 3t + 275 for 0 ≤ t ≤ 10.
Find and interpret the average rate of change of h over the interval [0, 10].Show work.
6.Mike wants to purchase custom-made pens to advertise his business. Two companies offer different deals:
Company A: Pay a design fee of $27.00, plus $0.18 per pen or Company B: Pay a design fee of $15.00, plus $0.24 per pen
(a) State a linear function f (x) that represents Company A's total charge for an order of xpens.
(b) State a linear function g(x) that represents Company B's total charge for an order of xpens.
(c) Mike wants to purchase 140 custom-made pens, as cheaply as possible. With which company should he place his order? Show work/explanation.
(d) For what number of pens 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)pens are ordered.
7. 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?
BRIEFLY EXPLAIN how you have decided which graph is the correct one.
(Grid supplied for scratch work; You are NOT required to submit your own graph)
8. (no explanation required)
Consider the graph of the piecewise function y = f (x) pictured below.
State the value of f (3).
(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. Based on data retrieved from https://www.erh.noaa.gov/lwx/climate/dca/dcatemps.txt the following chart of Washington, DC yearly average temperatures has been prepared.
The line of best fit, the regression line, is y = 0.0344x - 10.107, where x = year and y = average Washington, DC temperature, in degrees. The value of r2 is 0.6242.
(a) Use the regression line to estimate the average Washington, DC temperature in 1890, to the nearest tenth of a degree. Show some work.
(b) Use the regression line to predict the average Washington, DC temperature in 2018, to the nearest tenth of a degree. Show some work.
(c) In what year (to the nearest year) does the regression line predict an average Washington, DC temperature of 62.0 degrees? Show work, solving an appropriate equation.
(d) 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.
(e) 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?
10. Find all real solutions. Show work
z/2=4z2-1