How Do I Use This Activity?

This activity allows the user to manipulate a function graphically by using slider bars to change the value of the constants and coefficients in the function.

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Controls and Output

• The initial graph at the top of the activity is set to y = x. The coordinates of the black point on the function are printed beside the point. You can move the point left and right on the graph by using the blue slider bar below the graph.
  
  
  
• Enter the function you want to graph in the box marked y =. Any constant or coefficient you wish to be able to manipulate must be entered as a number. For instance, if you wish to experiment with the linear function y = x + 8 and wish to manipulate the coefficient of x it is necessary to type the equation as y = 1*x + 8 so the computer recognizes the multiplier as a parameter. Likewise if you wanted to experiment with the linear function y = 2*x and be able to manipulate the y-intercept it is necessary to type y = 2*x + 0. (Try typing in both and clicking the set function button so you can see the difference.)
  
  
  
• Use the following notations for the operations:
  
  

  Function	Symbol	Examples (including combinations of functions)
  addition	+	x + 3 x plus three
  subtraction	-	5 - x five minus x
  multiplication	*	(x - 2)*x x times x minus two
  division	/	3/x three divided by x
  power	^	x^3 - 1 x to the power of three minus one
  power	**	x**3 - 1 x to the power of three minus one
  π (pi)	pi	sin(pi*x) sin of π (pi) times x
  square root	sqrt(...)	sqrt(x-1) square root of x minus one
  nth root (see * below)	x^(1/n)	x^(1/3) cube root of x
  absolute value	abs(...)	abs(3 - x) absolute value of three minus x
  e to the power of x	exp(...)	exp(x) e to the power of x
  sine	sin(...)	sin(x**2) sine of x squared
  cosine	cos(...)	cos(5 - x) cosine of five minus x
  tangent	tan(...)	tan(x) tangent x
  arcsine	asin(...)	2*asin(x)   two times arcsine x
  arccosine	acos(...)	acos(x) arccosine x
  arctangent	atan(...)	atan(x) arctangent of x
  hyperbolic sine	sinh(...)	sinh(1 - x) hyperbolic sine of one minus x
  hyperbolic cosine	cosh(...)	cosh(10/x) hyperbolic cosine of ten divided by x
  hyperbolic tangent	tanh(...)	tanh(x) hyperbolic tangent of x
  natural logarithm	log(...)	log(x) natural logarithm of x
  base 10 logarithm	log10(...)	log10(x + 5) base ten logarithm of x plus five

  ^* When x is less than zero, the exponent must be written as a whole number or in fraction form, not a decimal. For instance, if you want to graph the fifth root of negative numbers, you must write x^(1/5), not x^(0.2).
  
  
• Beside the function is a checkbox labeled Exponents Change. If your function has an exponent which you want to remain constant and do not want to be able to manipulate the value of the exponent, leave the box unchecked.
  
  
• After entering the function, click on the Set Function button to the right of the input box. The computer graphs the function. The equation of the function appears below the graph where each constant is written in a different color. Slider bars will appear colored the same colors as the respective constants or coefficients which they manipulate.
  
  
• The Change Function button takes the user back to the first screen to make a change to the function or type in a new function altogether.
  
  
• The Reset Sliders button will place the sliders back in their original, central position after being used.
  
  
• To change the minimum and maximum of the slider bars, click the Slider Limits... button. This will display a window where you may set the minimum and maximum of each slider bar. You can also set the step size for each slider bar. The step size determines what values the slider bar will stop at. For instance, if you set the minimum to 0, the maximum to 1, and the step to 0.1, the slider will stop at 0, 0.1, 0.2, etc. However, if you set the step to 0.2, the slider will stop at 0, 0.2, 0.4, etc.
  
  
  
• To see a grid on the graph, check the Show Grid checkbox.
  
  
• You may set the graph boundries by clicking the Set Window... button. This will display a new window where you may enter new values for the x max, x min, y max, and y min. After you have entered your new settings, clicke the Set button. To return the graph boundaries to their defaults click the Get Defaults button followed by the Set button.
  
  
  
• Checking the Show Trace checkbox will leave old functions on the graph as you change the slider bars. For instance, suppose your function is y = 3*x+5. If you check Show Trace and then drag the slider bar for the slope through the values 3, 4, 5, and 6, all four functions (y = 3*x+5, y = 4*x+5, y = 5*x+5, and y = 6*x+5) will be visible at the same time. The Clear Trace button will remove the old graphs.