Whole Group: Basics of Graphing on your TI Calculator

Transcription

1 Whole Group: Basics of Graphing on your TI Calculator 1. Start by pressing the Y= key on the upper left of your calculator. Notice that there are 10 different lines to write; this means that it is possible to have 10 different graphs shown at once. 2. Put in the following three equations: a. y = 3x + 6 b. y = 3x 2 + 3x 2 c. y = 2 x x + 7 Use the X,T,θ,n key to represent your variable, x. 3. Now press the GRAPH button on the upper right. Your window should look like this: If not, your window settings may have been changed. Press ZOOM, then option 6 to reset your window to default view. 4. Notice that one of our graphs is barely visible near the top of the window. Let s try to fix this: a. One thing we can do is zoom in or out. Press ZOOM, then option 3 to zoom out. Zoom is a really easy way to adjust the window, but it is somewhat limited. b. We can also adjust the window manually. Press the WINDOW button, then set your window like so: This looks better than just zooming out, but is more time consuming.

2 c. One more option for adjusting the window is to use zoom-fit. Option 0 under the zoom menu will attempt to automatically detect the shape of the graph, and adjust the window accordingly. Zoom-fit does not work so well on this graph, but try it on the next one. 5. Clear all your Y= equations, and put in a new one: y = x 3 x 2 54x Be sure to adjust your window to get a good view of the graph (try zoom-fit). 6. When looking at the graph, you can move the cursor freely by using the arrow keys. If you press the TRACE key, the left and right arrow keys will trace along your curve. Try to approximate all x- and y-intercepts of the graph. x-intercepts: y-intercepts:

3 Station 1: Using the TABLE function In many situations, we cannot get enough information by just looking at the shape of a graph. The TABLE feature allows us to retrieve more numeric data from a graph. 1. Input the following equation into the Y= menu: y = 1.5x 3 5 x a. Select the TABLE menu by inputting the following keystrokes: 2 nd -> GRAPH Use the arrow keys to explore values. Notice what the calculator displays when you look at any negative values for x (why?). b. By default, your table will likely start at 0 and increment by 1 each line. However, you can adjust this by selecting the TBLSET key above the WINDOW key. Try setting your table as follows: This tells your calculator to start the table at 9.1 and go up/down by.05 on each row. c. Complete the table below for the equation y = 1.5x 3 5 x. x y d. Adjust your table settings to try to find the coordinates of the point where the graph s y- value is minimized (Hint: it s between x=0 and x=1).

4 2. Input the following two equations into the Y= menu: y 1 = x 1.2 3x + 2 y 2 = x x 64 (Note that the minus key is different from the negative key. Can you tell which is which?) 3. Complete the table. Be careful of displayed rounding on your calculator. Highlight the values to see their exact value. x y1 y

5 Station 2: Using the CALC function Not only can our calculators show us graphs of equations, but they also come equipped with many different numerical solving techniques. 1. Input the following equation into the Y= menu. Don t forget about order of operations; mind your parentheses!: y = x2 4 x 1 a. Select the CALC menu by inputting the following keystrokes: 2 nd -> TRACE This menu contains many useful tools, most of which we will explore at some point this year. Today, we will only look at the first two: value and zero. b. Option 1, value, allows us to enter in any x-value that is visible in the current window settings, and the calculator will show you that location on the curve as well as give its corresponding y-value. c. Use this function to complete the table below (you will need to zoom out for most of these): x y d. Now, under CALC, select option 2: zero. (A zero is another name for an x-intercept). e. You have probably noticed that our equation has two x-intercepts, so we need to help our calculator figure out which x-intercept we want to calculate. To do this, we need to specify three things: left-bound, right-bound, and guess.

6 i. For left-bound, use the left and right arrow keys to select a point on the curve to the left of the x-intercept. ii. For right-bound, select a point to the right. iii. For guess, select a point somewhere in the middle of your left- and rightbounds. You should get x = 2 and x = 2 for the two zeros. 2. Calculate all x- and y-intercepts of the following graph: y = 1 2 x3 4x + 2 (For the y-intercept, you can use CALC-> value with x = 0. Although you really don t need a calculator at all for this one)