Here is [code]g[/code], the model of an incoming missile you [url=https://www.geogebra.org/m/x39ys4d7#material/aayx7rmz]generated earlier[/url]. I've added a point [code]E[/code] at about time 20. I've also added the variable [code]h[/code], and displayed its slider. See the bottom of this page for how to create [code]h[/code] on your own outside of this book.[br][br]The algebraic code for [code]g[/code] is lot more complex than code for [code]f[/code] from [url=https://www.geogebra.org/m/x39ys4d7#material/mmyjmk4h]earlier in this chapter[/url], but since [code]g[/code] and [code]f[/code] are both functions, at their core they are the same: they are both mathematical computer programs that take a number as input, use algebra code for systematically modifying the input, return the resulting number as an output. Furthermore, since we're going to let Geogebra do all the heavy lifting, who cares if [code]g[/code] is complicated? [br][br]Let's try to study some limits related to the function [code]g[/code]. [br][br]Try creating a second point on [code]g[/code] using [code]h[/code] like [url=https://www.geogebra.org/m/x39ys4d7#material/mmyjmk4h]earlier in this chapter[/url]. Note that the point on [code]g[/code] is called [code]E[/code] now (not [code]A[/code])!

Sidenote: If you want to create [code]h[/code] on your own in Geogebra Desktop, just type [code]h=0[/code] into the input bar. Then in the Algebra Perspective, click the dot next to [code]h[/code] to display the slider bar. Right click (or CTRL click on a Mac) on [code]h[/code] to open its object properties. There you can adjust the range and increment of the slider for [code]h[/code]. For studying limits, I usually set the range from -1 to 1 in increments of 0.01. Download this file (click on the three dots in the top right) and see for yourself!