>Theory of Functions>How to Graph a Function in GeoGebra

How to Graph a Function in GeoGebra

To work with functions in GeoGebra, you can either use Algebra View and Graphics View together, or use CAS by itself.

When a function is entered into Algebra View, the graph automatically shows up in Graphics View.

The instructions below describe how you:

1.: Define a function.
2.: Define a function with a specific domain.
3.: Find $y$ when you have an $x$ -value.
4.: Find $x$ when you have a $y$ -value.

Note! Before using the instructions below, open Algebra View and Graphics View under View in Menu.

GeoGebra Instruction 1

Defining a Function

Type the function into Algebra View and press Enter. The function shows up in Algebra View, and the graph gets drawn in Graphics View.

GeoGebra Instruction 2

Defining a Function with a Specific Domain

Use the command

Function(<Function>, <Start x-Value>, <End x-Value>)

by typing it into Algebra View.

For <Function>, you type in the expression for the function (just like in GeoGebra Instruction 1). For <Start x-value>, you choose the $x$ -value at which you want the function to start, and for <End x-value>, you choose the $x$ -value at which you want it to end. When you type this in, you determine which points you want to have shown on the graph. The domain is often stated in the exercise.

GeoGebra Instruction 3

Finding $y$ from $x$

1.: Type the function from the exercise into Algebra View.
2.: Find the $y$ -value by typing $f (x_{1})$ in Algebra View, where $x_{1}$ is the $x$ -value you’ve been given in the exercise. If you’ve called your function something other than $f (x)$ —for example $h (x)$ —you have to write $h (x_{1})$ instead.

Screenshot of GeoGebra showing two graphs and the y-value of a function at x=1

GeoGebra Instruction 4

Finding $x$ from $y$ (Graphically)

1.: Type the function into Algebra View and press Enter. The expression for the function shows up in Algebra View and the graph gets drawn in Graphics View.
2.: Now you can write: $y = y_{1}$ in Algebra View, where $y_{1}$ is the $y$ -value you’ve been given in the exercise. Press Enter. A horizontal line shows up in Graphics View.
3.: You find the $x$ -values by determining the points of intersection between the line $y = y_{1}$ and the graph of the function by using the Intersect tool. The points will show up in Algebra View.
4.: Determine the $x$ -values by reading off the $x$ -values for the points of intersection.

Finding $x$ from $y$ (`CAS`)

1.: Open CAS under View in Menu.
2.: Type the function into CAS and press Enter.
Note! Remember to write := after the name of the function $(f (x)$ :=), otherwise, CAS won’t recognize the function in the command in the next step!
3.: Write $f (x) = y_{1}$ in CAS, where $y_{1}$ is the $y$ -value you’ve been given in the exercise, and press Solve or Solve Numerically to find the $x$ -value(s).
4.: If you get {} as the answer, it means that there are no $x$ -values for that $y$ -value.