Contents of Implicit Plots

Implicit Plots

The equation of a circle cannot be rewritten as a function of one variable. You can plot the set of points satisfying such an equation using the 2D implicit plot feature.

$\blacktriangleright$ To plot an equation

1.: Enter the equation.
2.: With the insertion point in the equation, from the Plot 2D submenu, choose Implicit.

The Domain Intervals for the following plot were set to -3≤x≤7 and -2≤y≤8.

$\blacktriangleright$ Plot 2D + Implicit

$\left(\vphantom{ x-2}\right.$ x - 2 $\left.\vphantom{ x-2}\right)^{{2}}_{}$ + $\left(\vphantom{ y-3}\right.$ y - 3 $\left.\vphantom{ y-3}\right)^{{2}}_{}$ = 25

itbpF2.0064in1.3361in0inFigure itbpF2.0046in1.3353in0inFigure

itbpF2.0046in1.3353in0inFigure

Unequal scales on the x- and y-axes can cause distortion of geometric figures. Click the Equal Scaling Along Each Axis box to make the figure on the left look like the circle (middle figure).
With the Domain Intervals unchanged, click to remove the check mark from the View Intervals + Default and edit the View Intervals to -10≤x≤10 and -10≤y≤10 in order to generate the plot above on the right. This again illustrates the difference between Domain Intervals (in this case, -3≤x≤7 and - 2≤y≤8) and View Intervals (in this case, -10≤x≤10 and -10≤y≤10).

You can make an implicit plot of the equation x = f (y) to plot the inverse function or inverse relation of a function y = f (x). For example, to plot the cube root function y = x, observe that it is the inverse function to y = x³ and do an implicit plot of x = y³.

$\blacktriangleright$ Plot 2D + Implicit

y³ = xdtbpF4.1355in2.0003in0pt

For the inverse relation of the sine function, do an implicit plot of x = sin y. Changing the view appropriately will give the plot of the inverse sine function.

$\blacktriangleright$ Plot 2D + Implicit

x = sin ydtbpF3in2.0003in0pt