blank     blank       Finding Limits Graphically and Numerically
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Input function f(x) =

Input value of c =


Limit from the left:


Limit from the right:


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1 2 3 x y Clear
4 5 6 t θ π
7 8 9 * +
0 . -(neg) ÷ ( ) (/)
2 3 4 5 6 ^
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Log 10x Ln e ex Submit
|  | Abs √ ̅ ∛ ̅ ∜ ̅ nroot
Fraction ( )/( ) Log/Log [[ ]] Radian
Mode
Degree
Mode

Restricting x and piecewise functions
{x ≤ } {x < } {x ≥ }
{x > } {x ≠ } {x = }
{a ≤ x ≤ b} {a ≤ x < b}
{a < x ≤ b} {a < x < b}
{ } x < > =

Restricting y
{y ≤ } {y < } {y ≥ }
{y > } {y ≠ } {y = }

Trigonometric and Hyperbolic Functions
Sin Cos Tan Csc Sec Cot
Asin Acos Atan Acsc Asec Acot
Sinh Cosh Tanh Csch Sech Coth
Radian
Mode
Degree
Mode
x y θ t
π

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Special Functions:

Greatest Integer Function
Example 1: Graph y = [[x]]; Input y = [[x]]
Example 2: Graph y = [[x + 2]]; Input y = [[x + 2]]
Example 3: Graph y = [[x - 3]]; Input y = [[x - 3]]
Note: Graph should be in "point mode".

Conic Sections: Circle, Ellipse, Hyperbola, Parabola               
Input Format: circle(h; k; r); where (h, k) is center of circle and r is radius
Example: (x - 4)2 + (y + 3)2 = 25; Input will be circle(4; -3; 5)
Example: x2 + y2 = 20; Input will be circle(0; 0; √ ̅(20))


              
Input Format: ellipse(h; k; value under (x - h)2; value under (y - k)2); where (h, k) is center of ellipse
Example: (x - 4)2/16 + (y + 3)2/9 = 1; Input will be ellipse(4; -3; 16; 9)
Example: (y - 2)2/25 + (x + 7)2/12 = 1; Input will be ellipse(-7; 2; 12; 25)


              
Input Format: hyperbolaXY(h; k; value under (x - h)2; value under (y - k)2);
where (h, k) is center of ellipse
Example: (x - 4)2/16 - (y + 3)2/9 = 1; Input will be hyperbolaXY(4; -3; 16; 9)
Example: x2/15 - y2/20 = 1; Input will be hyperbolaXY(0; 0; 15; 20)


              
Input Format: hyperbolaYX(h; k; value under (x - h)2; value under (y - k)2);
where (h, k) is center of ellipse
Example: (y - 6)2/16 - (x + 7)2/9 = 1; Input will be hyperbolaYX(-7; 6; 9; 16)
Example: y2/15 - x2/20 = 1; Input will be hyperbolaYX(0; 0; 15; 20)


Statistics Functions

              
Input Format: normalpdf(μ; σ) where μ is population mean and σ is population standard deviation
Example: Draw pdf for normal population with μ = 0 and σ = 1. Input will normalpdf(0; 1)
Example: Draw pdf for normal population with μ = 2 and σ = 5. Input will normalpdf(2; 5)

              
Input Format: normalcdf(μ; σ) where μ is population mean and σ is population standard deviation
Example: Draw cdf for normal population with μ = 0 and σ = 1. Input will normalcdf(0; 1)
Example: Draw cdf for normal population with μ = 2 and σ = 5. Input will normalcdf(2; 5)

              
Input Format: tdistpdf(DF) where DF is degrees of freedom
Example: Draw pdf for t-distribution with degrees of freedom of 15. tdistpdf(15)

              
Input Format: tdistcdf(DF) where DF is degrees of freedom
Example: Draw cdf for t-distribution with degrees of freedom of 15. tdistcdf(15)

For more statistics-related features, go to

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Plotting Points on Cartesian Plane          on/off
Point Size: Large      Medium      Small      
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( , )        for tracing feature (read only)





Graphing equation of circle in standard form (Video)
(x - h)2 + (y - k)2 = r2        on/off   
To view list of points on a graph, select a graph.
Example: Graph (x - 4)2 + (y + 2)2 = 16    

( )2     ( )2 =    on/off

( )2     ( )2 =    on/off

( )2     ( )2 =    on/off

( )2     ( )2 =    on/off

( )2     ( )2 =    on/off

( )2     ( )2 =    on/off

( )2     ( )2 =    on/off

( )2     ( )2 =    on/off

( )2     ( )2 =    on/off

( )2     ( )2 =    on/off









Graphing ellipse and hyperbola in standard form (Video)
(x - h)2/a2 + (y - k)2/b2 = c            on/off
  

( )2
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Parametric Equations Video                  on/off
Tmin =    Tmax =    Tstepsize =     
X(t) = on/off
Y(t) =

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Y(t) =

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Polar Equations Video                       on/off       
θmin =    θmax =    θstepsize =      
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r(θ) = on/off

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Plotting Points in polar coordinates (r, θ) Video   
Note: Use keypad below to indicate whether θ is in radians or degrees.
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blank     blank          point mode          line mode

Tracing for Cartesian Equations: ON    OFF         Video
To trace a graph, click on the radio button to the right of the input equation.

Note: When tracing feature is ON, shading feature is OFF.
Number of decimal places for input variable:
(Note: Input value of 0 means input variable will be integer.)


Parametric Equations Tracing:      Video      on/off
Select a pair of parametric equations:
                           
                           
  t = (click on arrow to start tracing)


Tracing for Polar Equations:      Video      on/off

Select an equation:

θ = (click on arrow to start tracing)








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Table of Values for Cartesian Equations
Finding specific y when x = Video
Finding specific x when y = Video
    Separate values with commas. Example: 2,3,7    

Express x in terms of π             Express y values as fractions             Detailed
TABLE 1
TABLE 2
TABLE 3
TABLE 4
TABLE 5
TABLE 6
TABLE 7
TABLE 8
TABLE 9
TABLE 10
TABLE 11
TABLE 12
TABLE 13
TABLE 14
TABLE 15
TABLE 16
TABLE 17
TABLE 18
TABLE 19
TABLE 20

Generate table of values:     Start =        End =        Stepsize =
   Video



Converting a value to a fraction or long decimal:
Convert to       










Table of Values for Parametric Equations

Tmin =      Tmax =      Stepsize =      on/off
     
Table of Values for Parametric Equations X(t) and Y(t) (set 1):
Table of Values for Parametric Equations X(t) and Y(t) (set 2):
Table of Values for Parametric Equations X(t) and Y(t) (set 3):
Table of Values for Parametric Equations X(t) and Y(t) (set 4):
Table of Values for Parametric Equations X(t) and Y(t) (set 5):
Table of Values for Parametric Equations X(t) and Y(t) (set 6):
Table of Values for Parametric Equations X(t) and Y(t) (set 7):
Table of Values for Parametric Equations X(t) and Y(t) (set 8):
Table of Values for Parametric Equations X(t) and Y(t) (set 9):
Table of Values for Parametric Equations X(t) and Y(t) (set 10):







Table of Values for Polar Equations

θmin =      θmax =      θstepsize =      on/off
 
Table of Values for Polar Equation 1:
Table of Values for Polar Equation 2:
Table of Values for Polar Equation 3:
Table of Values for Polar Equation 4:
Table of Values for Polar Equation 5:
Table of Values for Polar Equation 6:
Table of Values for Polar Equation 7:
Table of Values for Polar Equation 8:
Table of Values for Polar Equation 9:
Table of Values for Polar Equation 10:
Table of Values for Polar Equation 11:
Table of Values for Polar Equation 12:
Table of Values for Polar Equation 13:
Table of Values for Polar Equation 14:
Table of Values for Polar Equation 15:
Table of Values for Polar Equation 16:
Table of Values for Polar Equation 17:
Table of Values for Polar Equation 18:
Table of Values for Polar Equation 19:
Table of Values for Polar Equation 20:





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 xMin  xMax      
 yMin      yMax     
    

Location of Mouse Over Chart:
Location of Mouse Click: ( , )

blank     blank   Reflection of Cartesian Equations: Video            on/off
Select an equation:
Reflect graph over:
(Reflection is only for graph with equation that starts with "y = " or "x = ")

blank     blank   Rotation of Cartesian Equations: Video            on/off
Select an equation:
Degrees of rotation: (click on arrow to start rotation)
(Note: Rotation is only for graph with equation that starts with "y = " or "x = ")
( Rotation is about the origin; positive degrees of rotation is counterclockwise.)

blank     blank   Finding x-intercept and y-intercept: Video            on/off
Select an equation:
Search for x-intercept between x =    and   x =       

Search for y-intercept between y =    and   y =       


blank     blank   Finding Intersection of Two Graphs: Video            on/off
Select First Graph:
Select Second Graph:
Input approximate location of intersection (click on intersection or input manually): (    ,    )      

blank     blank   Finding Maximum or Minimum: Video            on/off
Select a graph:
For equation with "y = ":
Search for maximum/minimum point between x =    and    x =
     


For equation with "x = ":
Search for leftmost/rightmost point between y =    and    y =










blank     blank   Shading/Painting: Video            on/off
Enter Stroke Width:      (Enter a value between 1 and 100; default value is 5.)
Transparency Level:  (Enter a value between 0.1 and 1; default value is 0.4.)
Select a shading color:
Select a shading tool:


blank     blank   Drawing Line With Two Given Points:
Draw Line With Two Given Points:

Point 1: x1 = y1 =
Point 2: x2 = y2 =            

blank     blank   Drawing Line With Given Slope and One Point:
Draw Line With Given Slope and One Point:

Slope =
Point : x1 = y1 =            

blank     blank   Drawing Parabola Through Vertex and One Point:
Draw Parabola Through Vertex and One Point:

Vertex: x = y =
Point : x1 = y1 =            

blank     blank   Drawing Parabola Through Three Points::
Draw Parabola Through Three Points:

Point 1 : x1 = y1 =
Point 2 : x2 = y2 =
Point 3 : x3 = y3 =            

blank     blank   Drawing Circle:
Draw Circle:

Input Center : x = y =
Input Radius =                            

blank     blank   Drawing Ellipse of Equation in Standard Form:
Draw Ellipse of Equation in Standard Form:

Center : h =     k =
Value Under (x - h)2 =
Value Under (y - k)2 =
       

blank     blank   Drawing Hyperbola of Equation in Standard Form:
Draw Hyperbola of Equation in Standard Form:

Center : h =     k =
Value Under (x - h)2 =
Value Under (y - k)2 =
If equation is of the form (x - h)2/a2 - (y - k)2/b2 = 1, then
If equation is of the form (y - k)2/a2 - (x - h)2/b2 = 1, then
   

blank     blank   Drawing Two Parralel Lines:
Draw Two Parralel Lines:

Line 1 :
Slope =              Passing Through: x = y =

Line 2 (parallel to Line 1; same slope as Line 1) :
Passing Through: x = y =
   

blank     blank   Drawing Two Perpendicular Lines:
Draw Two Perpendicular Lines:

Line 1 :
Slope =              Passing Through: x = y =

Line 2 (perpendicular to Line 1; slope is negative reciprocal of slope of Line 1) :
Passing Through: x = y =
   

blank     blank   Testing Point for Inequality and Equation:
Testing Point: Input x- and y-coordinate (click on grid to input):
x =     y =      





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Video








Input for all eight graphs
3x + 4 - 5
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y = 2|3.2x + 4/5| - 6
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How To Save Image To Disk:
1) Place mouse over chart; 2) Right click; 3) Select 'Save Picture As' or 'Save Image As'