This tool can be used to investigate rational functions, like those in
Whelk-Come to Mathematics, or exponential functions, as found in
Shedding the Light or
Trout Pond. It can also be used to investigate any other functions that can be explored with a graphing calculator or spreadsheet software.
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Click on the Y= or Plots tab. In this section, you can choose which of three types of relationships to graph:
| Y=
| In Y1 through Y5, you can enter an algebraic function to be graphed. Use + for addition, - for subtraction, * for multiplication, / for division, and ^ to raise an expression to a power. For instance, to represent the equation y = 3(x – 2)3 + 4, you would enter 3 * (n ‑ 2) ^ 3 + 4. In addition, the constants a, b, and c can be used within these functions to allow further investigation. For instance, if the equation for Y1= is entered as 3*a, then the graph of the function can be adjusted using the slide for a on the Graph tab.
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| Next=
| For each Next equation, you can enter a Now-Next function to be graphed. These are recursive functions such as Next = Now7nbsp;+ 5, which means that the Next value is equal to five more than the current (Now) value. (If you do not enter a value for "Starting At" the first value is assumed to be 0.)
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| Plot
| By checking the boxes for Plot1 through Plot5, you can indicate that columns from the Data tab should be graphed against one another.
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The Data tab can be used to access the spreadsheet. Data in columns 1‑4 can be graphed by choosing the Plots in the Y= or Plots tab.
Select the Graph tab to see a graph of the functions selected under the Y= or Plots tab. (The sliders for a, b, and c can be adjusted to investigate various functions, if these constants have been used in the Y= or Plots tab. For instance the function Y1 = a*x+b can be entered, and the sliders can then be used to investigate linear functions of the form y = ax + b.)
The Window tab can be used to adjust which portion of the graph is displayed. Highlighting the "Show Legend" box will label each function.
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Select the Y= or Plots tab, and enter the following function:
Y1 = a * x + b
This is the general form of a linear equation, where a is the slope of the line and b is the y‑intercept.
Click on the Graph tab, and adjust the values for a and b using the sliders at the bottom of the screen.
- How does the value of a affect the graph of the line? How does the line change when a is positive or negative?
- How does the value of b affect the graph of the line? How does the line change when b is positive or negative?
- Predict what the line for y = ‑3x + 8 will look like. Test your conjecture using the sliders to make a = ‑3 and b = 8.
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