Project 4.1 Transformations of
Linear Functions
Investigate how the constants a and b affect the graph
of y = x in the equation y = ax + b.
Note:
If you have a TI-83 Graphing Calculator, clear all the Y= entries before graphing each new set of linear functions in the project's
questions. The calculator will display the graphs in order.
The graph of Y1 will be displayed first, followed by Y2,
etc. Set Y1, Y2 and Y3 to graph a
dotted, solid and thick line respectively.
Suggested dimensions of the viewing window for this project are [–10,
10], Xscl = 1 and Yscl = 1, i.e. use ZOOM 6.
1a. Graph the following linear functions on the same set of
axes:
b. How are the graphs alike?
c. Where does each graph cross the y-axis?
d. What happens to the graph of y = x when a
constant is added?
e. What does b do in y = x + b?
2a. Graph the following linear functions on the same set of
axes:
b. How are these graphs alike?
c. How are these graphs different?
d. What happens to the graph of y = x when x is multiplied by a positive number greater than 1?
e. What does a do in y = ax when a > 1?
3a. Graph the following linear functions on the same set of
axes:
b. How are these graphs alike?
c. How are these graphs different?
d. What happens to the graph of y = x when x is multiplied by a negative number less than –1?
e. What does a do in y = ax when a < –1?
4a. Graph the following linear functions on the same set of
axes:
Note:
If you are using a TI-83 Graphing Calculator, you must enclose a
fraction in parentheses or brackets.
b. How are these graphs alike?
c. How are these graphs different?
d. What happens to the graph of y = x when x is multiplied by a positive number between 0 and 1?
e. What does a do in y = ax when 0 < a < 1?
5a. Graph the following linear functions on the same set of
axes:
Note:
If you are using a TI-83 Graphing Calculator, you must enclose a
fraction in parentheses or brackets.
b. How are these graphs alike?
c. How are these graphs different?
d. What happens to the graph of y = x when x is multiplied by a negative number between –1 and 0?
e. What does a do in y = ax when –1
< a < 0?
6a. Graph the following linear functions on the same set of
axes:
b. Describe how the constants 2 and 3 affect the graph of y = x.
7a. Graph the following linear functions on the same set of
axes:
8a. Graph the following linear functions on the same set of
axes:
b. Describe how the constants –2 and 3 affect the graph
of y = x.
9a. Graph the following linear functions on the same set of
axes:
10. Write an equation of your own in the form y = ax + b and describe how each constant
affects the graph of y = x.
11.
Generalise by describing how a and b affect the graph of y = x in the equation y = ax + b. |
