We were given a worksheet on modifying functions with the equation y=Af(Bx+C)+D.
The first function we're given is y1=f(x)= x + x^2 and we're supposed to graph it. Then we're told to graph y2=2f(x), and we're given instructions on how to enter it [y2=2 ->vars->y-vars->function->Y1->enter].
After that we're supposed to enter and graph Y2=f(2x), Y3= f(.5x), Y4= f(-x), and after that we have to graph Y2= f(x-2), Y3= f(x+2), Y4= f(2x+2)
The problem is, it doesn't tell us how to enter these new variations and I can't figure out how to do it on my calculator [I'm using a TI-83 plus]! Can someone tell me how to enter them [if you could just model one from each set, that would be great]?
Sure! I can help you with that. Here's how you can enter and graph each of the new variations on your TI-83 Plus calculator:
1. Y2 = f(2x):
- Press the [Y=] button to enter the equation editor.
- Clear any existing equations.
- Enter "Y2=" on the left side.
- Press the [ALPHA] and then the [WINDOW] button to access the VAR-LINK menu.
- Scroll down to the "f(" option and press [ENTER].
- Enter "2X" inside the parentheses (without the quotes).
- Press [ENTER] to save the equation.
- Graph the equation by pressing the [GRAPH] button.
2. Y3 = f(0.5x):
- Follow the same steps as above for entering Y2 = f(2x), but this time replace "2X" with "0.5X" inside the parentheses.
3. Y4 = f(-x):
- Clear any existing equations.
- Enter "Y4=" on the left side.
- Press [(-)] for the negative sign.
- Press [ALPHA] and then the [WINDOW] button to access the VAR-LINK menu.
- Scroll down to the "f(" option and press [ENTER].
- Enter "X" inside the parentheses.
- Press [ENTER] to save the equation.
- Graph the equation by pressing the [GRAPH] button.
4. Y2 = f(x-2):
- Clear any existing equations.
- Enter "Y2=" on the left side.
- Press [ALPHA] and then [ALPHA] again to access the lowercase alphabets.
- Press the "[X,T,θ,N]" button to select "x".
- Press the subtraction [-] button.
- Enter "2".
- Press [ALPHA] and then the [WINDOW] button.
- Scroll down to the "f(" option and press [ENTER].
- Enter "X" inside the parentheses.
- Press [ENTER] to save the equation.
- Graph the equation by pressing the [GRAPH] button.
5. Y3 = f(x+2):
- Follow the same steps as above for entering Y2 = f(x-2), but this time replace the subtraction with an addition symbol [+].
6. Y4 = f(2x+2):
- Clear any existing equations.
- Enter "Y4=" on the left side.
- Press [ALPHA], select "[X,T,θ,N]", and press [ENTER] to enter "2X".
- Press the addition [+] button.
- Enter "2".
- Press [ALPHA] and then the [WINDOW] button.
- Scroll down to the "f(" option and press [ENTER].
- Enter "X" inside the parentheses.
- Press [ENTER] to save the equation.
- Graph the equation by pressing the [GRAPH] button.
These steps should allow you to effectively enter and graph each variation of the function on your TI-83 Plus calculator. Repeat these steps for the other variations, replacing the equation and Y-variable with the appropriate values.
I hope this helps you with your worksheet! Let me know if you have any other questions.
Sure! I can help you enter and graph these variations on your TI-83 Plus calculator. Let's go through each of the variations step-by-step:
1. Y2 = 2f(x):
To enter this variation, follow these steps:
- Press the "Y=" key.
- In the Y1 field, you'll see the equation for y1=f(x) (x + x^2). Overwrite it with "2*(x + x^2)".
- Press "GRAPH" to see the graph of Y2 = 2f(x).
2. Y2 = f(2x):
To enter this variation, follow these steps:
- Press the "Y=" key.
- In the Y2 field, enter "x + x^2" (since we want to graph f(x)).
- Press "VARS", then move the cursor to "Y-VARS" and press "ENTER".
- Select "1: Function" and press "ENTER".
- Scroll down to highlight "Y1" and press "ENTER".
- Overwrite "x" in the equation with "2x".
- Press "GRAPH" to see the graph of Y2 = f(2x).
3. Y2 = f(x-2):
To enter this variation, follow these steps:
- Press the "Y=" key.
- In the Y2 field, enter "x + x^2" (since we want to graph f(x)).
- Replace "x" with "(x-2)" in the equation.
- Press "GRAPH" to see the graph of Y2 = f(x-2).
4. Y2 = f(2x+2):
To enter this variation, follow these steps:
- Press the "Y=" key.
- In the Y2 field, enter "x + x^2" (since we want to graph f(x)).
- Replace "x" with "(2x+2)" in the equation.
- Press "GRAPH" to see the graph of Y2 = f(2x+2).
By following these steps, you should be able to enter and graph these variations on your TI-83 Plus calculator. Repeat the process for the remaining variations Y3 and Y4.
Remember to adjust the other variations by following the same steps but changing the equation accordingly.