|Module 1 - Describing Functions|
|Introduction | Lesson 1 | Lesson 2 | Lesson 3 | Self Test|
|Lesson 1.2: Describing Functions Graphically|
In Lesson 1.1 you defined the function f(x) = 2x2 - 5x - 3 and found its roots using Guess and Check and by factoring. In this lesson you will display this function graphically and use the graph to find the zeros of the function.
Graphing a Function
Functions must be defined in the Y= editor before they can be graphed. Even if you turned off your calculator after completing Lesson 1.1, the function f(x) = 2x2 - 5x - 3 should still be defined in Y1.
Setting the Viewing Window
Before you graph the function, you need to specify the
The values of the parameters of the viewing window determine the size of the portion of the coordinate plane displayed on the Graph screen.
The window values shown above are appropriate for our function's graph, so we will keep them. If you need to change your window values to match those shown above, you can do this by moving the cursor to the appropriate line with the cursor movement keys and then entering the desired values.
Displaying a Graph
Display the graph once the window values are set.
x-Intercepts and Zeros of f
In general for any real number r, r is a zero (or root) of f if and only if r is an x-intercept of the graph of f.
Finding Zeros Graphically
You can find the zeros of the function from the Graph screen by using the Zero feature, which will return the value of an x-intercept.
You will see the graph and a prompt for a left bound of an interval on the x-axis, as shown below. You must identify an x-interval containing the desired zero by specifying the left and right endpoints of the interval. It's not important that the interval be small, but the goal is to choose an interval that contains only one zero of the function. Otherwise, you might not find the zero you are looking for.
Begin by finding the larger of the two x-intercepts.
After you press , a small marker appears at the top of the Graph screen above the left bound of the interval, as shown below. The calculator then asks you to indicate the right bound of the interval.
After you press , another small marker appears at the top of the Graph screen above the right bound. The calculator then asks you to indicate an initial guess for the root.
The zero (or root) is x = 3, as shown at the bottom of the screen.
1.2.1 Use the CALCULATE Zero feature on the Graph screen to find the other root. Click here for the answer.
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