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. Below the graph is a slider bar and a box in which to enter a function. The slider bar can be moved left and right with the mouse, and permits the user to change the location of the point along the function.
  
  
• Type in a function. 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).
  
  
• Beneath the function is a check box 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. As well, a blue slider bar appears which manipulates a point along the curve, giving the coordinate as the point moves along the curve.
  
  
• The slider bars minimum and maximum values are determined by the place value of the last significant digit of the corresponding constant or coefficient. The computer identifies the place value and then adds and subtracts the next place value greater to determine the maximums and minimums. For example:
  
  
  • Enter the function y = 1200*x
  • The coefficient of x is 1200, which has 2 significant digits.
  • The 2 is the last significant digit and is in the hundred's place.
  • The thousands place is the next place value greater than the hundreds place
  • Therefore the computer adds and subtracts 1000 to 1200 to determine the minimum and maximum values of the slider bar.
  • The slider minimum is 200 and maximum is 2200.
  • If the constant or coefficient were 0.12 the computer would add and subtract one tenth to 0.12 because the last significant digit is in the hundredths place. (One tenth is the next place value greater than one tenth.) The minimum and maximum therefore would be 0.02 and 0.22 respectively.
  
  
  
• The "Show Trace" check box, when activated, allows the user to see the various intermediate stages as the function is manipulated by the slider bars. The "Clear Trace" button will remove the lines drawn after the show trace box has been activated.
  
  
• The "Reset Sliders" button will place the sliders back in their original, central position after being used.
  
  
• 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 "Set Window" button opens a new window so the x and y ranges of the graph can be changed. After setting the range values the sliders will automatically reset to their original positions.