Entering Functions in Graphing Tools

Getting Started

• Access the quick function entry screen by pressing the button or clicking the right mouse button
• Type a function into the Functions box. Each line is a separate function.
• Press Enter
• Adding “y=” to the front of the function definition is optional for Cartesian functions (but not other types of functions or inequations)

Entering Functions

• Most occasions, you can type the equation as you see it and the graph tool will interpret it correctly
• There are a limited number of codes and keywords you need to learn to enter every possible function

Codes to Remember

• Use codes as follows:
  • =
  • >=
  • <
  • / (followed by a space)
  • pi
  • th
  • sqrt
  • 3root

Fractions

• Use / key for fractions
• Complex numerators or denominators must be surrounded with brackets

Spaces in Functions

• Spaces can determine the meaning of functions
  • sin2 x equals sin x^2
  • sin 2x equals sin(2x)

Polar Functions

• Enter polar functions using r and th (which will be shown as )
  • Example: r = 2sin2 3th

Inverse Functions

• Enter inverse functions by typing x in terms of y or theta in terms of r
  • Example: x = 12/y

Inequations

• Can be drawn for Cartesian, Inverse and Polar graphs.
• Replace the = with >=, or <
• Example: y >= 3x - 7

Parametric Functions

• Enter the x and y components in terms of t. Separate with a comma
  • Example: x = sin t; y = cos 3t
• Parametric functions are graphed with a default domain of 0  t  20 unless otherwise specified

Implicitly Defined Relations

• The graph tool can graph any function expressed in terms of x & y
• If the graph tool cannot rearrange the relation, it will graph the relation using a different technique that restricts the analysis that the graph tool can perform

Complex Numbers

• Enter complex numbers in terms of z and i OR cis
  • Example: z4 = 25 + 4i

Slope Fields

• Include y’ in your function
  • Example: y' = 3x + 2y

Plot as Points

• Plot most functions as points on the plane.
• This option is available in the Function Properties screen.