The transformation of graphs

9/25/12

Every function is based off a parent function. These parent functions are then modified to create the new function. For instance:

 Use the function f(x) = x^2 + 3. The parent function for this is f(x) = x^2. As with the equation y = mx + b, the 3 here is the y intercept, or where the graph will begin at when x=0. The new graph should look something like this.

 

 

 

For horizontal movement, it works a little bit differently. If the number is placed with x in parenthesis, the number will affect where the graph starts on the x axis. A positive number shifts the graph to the left, and vice versa. An example is y = (x – 1)^2.

 

 

Graphs can also be reflected. The graph of y = x^2 may look like this:

We can reflect this graph by adding a negative sign in front of the x. this would look like y = - x^2, or:

 

 

Finally, graphs can become wider or narrower. Take the parent function of f(x)=IxI.

The initial function looks like:

 

 

 

By multiplying the absolute value of x by two, the graph becomes much narrower because the y increases much more rapidly, so f(x)=2IxI looks like: