Radical functions can be written as having a vertical stretch or a horizontal stretch. In Try This 4 you looked at the radical functions and and discovered that the graphs of these two functions are the same. When you look at the functions, you can see how the second function can be rearranged to be the same as the first function.

 

You can compare these functions to the function and describe the function as having a vertical stretch by a factor of 2.

 

 

When you compare to you can describe the transformation as a horizontal stretch by a factor of

 

 

Even though the stretches are different, the resulting graphs are the same. Note: When analyzing radical functions, any stretch can be described as either a vertical stretch or a horizontal stretch.

 

Self-Check 3

1. Consider the function
   1. Describe the transformation represented by f(x) as compared to Answer
   2. Write a function equivalent to f(x) in the form Describe the transformation represented by g(x) as compared to Answer
   3. Graph both functions f(x) and g(x). How do the graphs compare? Answer

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Up to this point, you have graphed radical functions using transformations. Now you will look at a graph and determine the radical function. View Determining a Radical Function from a Graph, which shows an example of how to write the radical function from a graph.