Before doing this activity. . .

What type of curve did you sketch?


Step 2.  Enter the following functions
into the
editor.
Graph the functions by pressing
and selecting 6:ZStandard. Sketch the graphs on your recording
sheet.
As the coefficient of x increased, what happened to the graph of the parent function ? 

Step 3.  Enter the following functions
into the
editor.
Graph the functions by pressing
and selecting 6:ZStandard. Sketch the graphs on your recording
sheet.
As the coefficient of x decreased, what happened to the graph of the parent function ? 

Step 4. 
What happened to the graph of the parent function when the coefficient of x became negative?


Step 5.  Enter the following functions
into the
editor.
Graph the functions by pressing
and selecting 6:ZStandard. Sketch the graphs on your recording
sheet.
As the absolute value of the coefficient of x increased, what happened? Does this graph look like the reflection of any previous graphs you have sketched? 

Step 6.  Enter the following functions
into the
editor.
Graph the functions by pressing
and selecting 6:ZStandard. Sketch the graphs on your recording
sheet.
As the absolute value of the coefficient of x decreased, what happened?

Let's summarize what we have "discovered" in Steps 1  6.
All of the functions you entered in these steps were of the form . We investigated what happened when a increased and decreased. Fill in the following blanks on your recording sheet.
When a is positive, the graph is that of a(n) _______________ function.
When a is negative, the graph is that of a(n) _______________ function.As a increases, the graph becomes more _______________.As a decreases, the graph becomes more _______________.
Step 7.  Enter the following functions
into the
editor.
Graph the functions by pressing
and selecting 6:ZStandard. Sketch the graphs on your recording
sheet.
What happened to the graph of the parent function when you increased the value being added to x? The value being added on is called the constant term. Did the graphs cross above or below the origin along the vertical axis? 
Step 8.  Enter the following functions
into the
editor.
Graph the functions by pressing
and selecting 6:ZStandard. Sketch the graphs on your recording
sheet.
What happened to the graph of the parent function when you decreased the value of the constant term? Did the graphs cross above or below the origin along the vertical axis? 
Let's summarize what we have "discovered" in Steps 7  8.
All of the functions you entered in these steps were of the form . We investigated what happened when c increased and decreased. Fill in the following blanks on your recording sheet.
As c increases, the graph shifts _______________.As c decreases, the graph shifts _______________.When c is positive, the graph will cross _______________ the origin along the vertical axis.
Let's put this all together now by answering the following practice problems. (Note: You will be asked to answer questions regarding these practice problems at the end of the activity.)When c is negative, the graph will cross _______________ the origin along the vertical axis.
Practice 1.  Given ,
answer the following without graphing.


Practice 2. 


Practice 3. 


Practice 4.  Without the use of a graphing
calculator, match the most appropriate graph for the function .


Practice 5.  Susie graphed the function
in her calculator. This is what her screen looked like.

LOOKING
BACK:
This activity investigated
linear functions. All of the linear functions that were investigated
were of the form ,
called the slopeintercept form. The coefficient of x, a,
is also called the slope of the line. The slope is the measurement
of the steepness or incline of the line. As you discovered, the larger
the absolute value of the slope, the steeper or the more inclined the line.
Whether the slope is positive or negative determines if the line will go
up or down from left to right. The constant term, c, is also
called the vertical axis intercept (or yintercept) because it determines
where the line will cross the vertical axis. If c is positive,
then the line will cross the vertical axis above the origin. and if c
is negative, then the line will cross the vertical axis below the origin.
Upon completing this activity, you can now predict what the graph of a linear function will look like before you ever graph it. Why is this important? One reason is so that you catch any errors. If you know roughly what the graph should look like before graphing it, then when a calculator or a computer gives you the "wrong answer" you will be able to catch the error. Another reason is so that you can view your graph. Not all window settings in a graphing calculator will allow you to "see" all the graphs. If you know something about the graph, you can set the appropriate window so that you can view it. The third reason, and probably the most important for a teacher, is so that you can manipulate your graph. If your line is inclined just the way you want it but, you would like to shift it up two units, what do you do? Right, add a 2 to the constant term. If your line is crossing the vertical axis at the appropriate location, but you would like to lessen its incline, what do you do? You reduce the value of the slope. As you will see later, this idea of manipulating the coefficients to control a graph, can be extended to other functions besides linear.
QUESTIONS:
After completing this activity,
prepare your responses to the following questions.
NEXT:
This is the end of the unit
learning activities. The next step is to complete the assessment
for this unit (go to the top of the page and click on Assessment).