Horizontal Expansions and Vertical Compressions

Hai guys! It's Shelly from JGMS and I will be covering the Horizontal Expansion and Vertical Compression part of our project. Before I show you how to graph a function with a horizontal expansion and a vertical compression, there are some things you guys should know.

Horizontal Expansion: The name pretty much explains it, it implies to the expansion of the graph on the x-axis.

Vertical Compression: The same thing can be said for a vertical compression, except it "shrinks" vertically and "stretches" horizontally.

Shape: If (a) = 1, then the curve will be basic, if (a) > 1, the curve will be narrow, and if (a) < 1, the curve will be wide.

     OKAY! LET'S GET STARTED!

       Graph all 3 functions.


     Basic: f(x)=x^2
      This graph represents a basic function, which we all should know before we learn how to graph horizontal expansions and a vertical compressions. (for a quick review check out jhelene's blog post or click this link jhelene's post on basic functions)

       

       Horizontal Expansion: f(x)=1/3x^2
       Since we know that (a) is < 1, our function should be "wide". To prove our theory, let's construct a table.  To find the y-value, fill in the function f(x)-1/3x^2 and fill in (x) with the x-values on the table.

       Now that we know our y coordinates, we must sketch a graph.

       

      
Vertical Compression: f(x)=2x^2

      Since we know that (a) > 1, our curve must be narrow. To prove this we must construct a x and y-values table. To figure out the y-values, use the function f(x)-2x^2 and fill in (x) with the x-values on the table.

 Now that we know our y-values, sketch a graph.

            
        

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