General - Graph Continuous vs Discrete Functions

A continuous function allows the x-values to be ANY points in the interval, including fractions, decimals, and irrational values.

A discrete function allows the x-values to be only certain points in the interval, usually only integers or whole numbers.:

Graph the continuous function:
y = x²for all Reals.

• Enter the function into "y=".
• Choose the window. ZOOM #6 (standard)
• Graph

disGraph1

Notice that all of the visable points are connected with a continual drawing.

Graph the discrete function:
y = x²for all Integers.

• We cannot limit the point choices in "y=". We need a different approach, the scatter plot.
• If your viewing window is the standard 10x10 window, you will have to determine which points will be visible in this window:
(x = -3, -2, -1, 0, 1, 2, 3)
• STAT - Edit - enter x (L₁) and y (L₂) values.
• Stat-Plot - Plot 1 - turn Plot "On" - Choose "Type" scatter plot (first icon) - Xlist: L1 - Ylist: L2 - choose any Mark.
• Choose ZOOM #9 (statistics)
• Graph

discrete3

disgraph2

Notice that only the integer values are plotted. The points are NOT connected.