i am attempting to graph the piecewise function
y=(-2/3)x-6 if -9<=x<-6
(1/3)x if -6<=x<0
(((x-3)^2)/9) + (((y-0)^2)/16)=1 if 0<=x<=6
on a ti 89 titanium. i believe you must use the when( feature, but i haven't a clue as to how. we are using transformations of piecewise functions and i wish to use this to check my graphs
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Sra
To graph a piecewise function on a TI-89 Titanium calculator, you can use the `when(` feature in the calculator's graphing mode. Here's how you can input and graph the given piecewise function:
1. Press the `APPS` button on your calculator.
2. Scroll down and select the `Data/Matrix Editor` application by pressing `ENTER`.
3. In the Data/Matrix Editor, press `F1` to create a new function. Give it a name like "func" and press `ENTER`.
4. Now you will define the piecewise function by splitting it into different sections.
- For the first segment, y = (-2/3)x - 6, use the following syntax:
`If(-9<=x<-6, -2/3*x - 6, <expression for other cases>)`.
- For the second segment, y = (1/3)x, use the following syntax:
`If(-6<=x<0, 1/3*x, <expression for other cases>)`.
- For the third segment, (((x-3)^2)/9) + (((y-0)^2)/16) = 1, use the following syntax:
`If(0<=x<=6, (-9((x-3)^2)/16)^0.5, <expression for other cases>)`.
5. After defining all the segments, press `F5` to exit the Data/Matrix Editor.
Now you can proceed to graph the piecewise function:
1. Press the `Y=` button on your calculator.
2. Clear any existing equations by selecting them and pressing `CLEAR`.
3. On the first line, enter `func(x)`.
4. On the second line, enter `when(` followed by each segment of the piecewise function, separated by commas, along with their respective conditions.
- For the first segment, `when(-9<=x<-6, -2/3*x - 6)`.
- For the second segment, `when(-6<=x<0, 1/3*x)`.
- For the third segment, `when(0<=x<=6, (-9((x-3)^2)/16)^0.5)`.
5. Press `GRAPH` to see the graph of the piecewise function.
Make sure to adjust the window settings if needed to view the entire graph. You can use the arrow keys to navigate and zoom in/out if necessary.
By following these steps, you should be able to graph the given piecewise function on your TI-89 Titanium calculator and compare it with your manually graphed functions to check for accuracy.