Essential Questions /
Go to page 193 in your book and read the problem at the top of the page to answer the following questions.
- A. Complete the following table in which V represents the value of the car after n years of ownership.
0
1
2
3
5
8
b. Is the value of the car a function of the number of years of ownership? Explain.
c. What is the independent variable? What is the dependent variable?
2. a. Select two ordered pairs from the table above and determine the average rate of change.
b. What are the units of measure of the average rate of change?
c. What is the practical meaning of the sign of the average rate of change?
d. Select two different ordered pairs and compute the average rate of change.
e. Select two ordered pairs not used in parts a or d, and compute the average rate of change.
f. Using the results in parts a, d, and e, what can you say about the average rate of change over any interval of time?
3. a. Is the value, V, of the car a linear function of the number of years, n, of ownership? Explain using the definition of linear function.
b. Is this function increasing, decreasing, or constant?
4. Graph the data from the table in problem 1 on an appropriately scaled and labeled set of axes. Connect the points to see if there is a pattern.
***The graph of a linear function is a nonvertical line. Remember that the constant rate of change is called the slope of the line and is denoted by the letter m.
5. a. What is the slope of the line graphed in problem 4?
b. What is the relationship between the slope of the line and the average rate of change.?
c. What is the practical meaning of the slope in this situation?
Definition
Vertical Intercept (y- intercept):
6.a. Using the table of data in Problem 1 or the graph in Problem 4, determine the y-intercept.
b. What is the practical meaning of the y-intercept in this situation? Include units.
7. a. Review how you determined the value, V, of the car in Problem 1 for a given number of years, n, of ownership. Write an equation for V in terms of n that models this situation.
b. Use your graphing calculator to sketch a graph of this equation. Use the window Xmin =-2, Xmax = 16, Ymin= -500, and Ymax = 25000
c. How does this graph compare to your graph in Problem 4?
8. Recall that the slope of your line is m = -1385 and the y-intercept is (0, 20,025). How is this information contained in the equation of the line you determined in Problem 7a?
Definition:
Slope-intercept form –
9. Identify the slope and y-intercept of the line whose equation is given. Write the y-intercept as an ordered pair.
a. b.
c. d.
Definition
Horizontal intercept (x –intercept):
Ex: Using the equation y=2x-10 find the y-intercept and the x-intercept
Sketch the graph using the intercepts
10. a. Determine the x-intercept of the graph of the car value equation
b. What is the practical significance of the x-intercept? Include units.
Definition
Zeros –