1. Which of these graphs are graphs of functions?
(no explanation required.) (There may be more than one graph which represents a function.)
2. A tank held 300 gallons of heating oil at the beginning of the month. 30 days later, 120 gallons remained in the tank. Find the average rate of change of heating oil per day. Show work.
A. - 6 gallons per day
B. - 4 gallons per day
C. 6 gallons per day
D. 10 gallons per day
3. State the center and the radius of the circle represented by the equation
(x + 1)2 + (y - 9)2 = 100
4. Solve the inequality 7 - (3 - 4x) ≤ 2(5 + 6x). Write the solution set in interval notation.
5. Consider the following graph of y = f (x). (Some of the points are plotted with using dots, for your convenience.) (no explanations required)
(a) State the y-intercept(s).
(b) State the value of f (-1).
(c) State the domain.
(d) State the range.
6. Find the slope-intercept equation for the line pictured below. Show work/explanation.
7. Let g(x) = x -5/x -1
(a) Calculate g(-3).
(b) State the domain of the function g(x) = x - 5/ x - 1
8. Consider the linear equation 4x - 6y = 9.
(a) Write the linear equation in slope-intercept form.
(b) State the value of the slope.
(c) State the y-intercept for this line.
(d) State a point on this line other than the y-intercept. (There are infinitely many right answers! Just state one of them.)
9. Hal earns a weekly paycheck consisting of base pay of $450, plus a commission of 7.2% of his weekly sales in excess of $6,000. (So, Hal only earns the commission only on the amount of sales over $6,000).
(a) Write an equation that can be used to determine Hal's weekly paycheck P, given the amount of weekly sales, x.
(b) Determine Hal's weekly paycheck if his weekly sales are $17,280. Show work.
(c) Determine Hal's weekly sales if his weekly paycheck is $898.20. Show work.
10. Consider the points (7, -1) and (4, 5).
(a) State the midpoint of the line segment with the given endpoints.
(b) Find the distance between the points. Show some work. Give the exact answer (involving a radical), simplify the radical as much as possible, and also state an approximation to three decimal places.
(c) Find the slope-intercept equation of the line passing through the two given points. Show work.
(d) If a line is perpendicular to your line in part (c), what would the slope of that line be? (no work/explanation required) [Section 43-50, Chapter 1 examples]
11. 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 the following chart of U.S. life expectancy for females has been prepared.
The regression line is y = 0.151x - 222.26, where x = birth year and y = U.S. female life expectancy, in years. The value of r2 is 0.9366. [Section 1.4, pages 114-117, Project-Linear Model conference]
(a) Use the regression line to estimate the U.S. life expectancy of a female baby born in 1990, 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 2019, 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? Since the line has a positive slope, r is positive.