x^n when n is not an integer - getting to the root of things
- Judah L Schwartz
What happens if the n in the function is not an integer? We know from the rules of combining exponents that times is x. This means that is the same as the square root of x. As you slide the slider, you will see that some graphs are plotted for both positive and negative values of x and some graphs for positive values only. Why? Are there any functions of the form where n is not an even integer that have values for negative x? Challenge - For each power of x you explore check and uncheck the absolute value functions checkbox. How would you characterize the difference between f(x) and absolute value of f(x) – which is written as | f(x) | In general, do you believe that |f(x)| and f(|x|) are the same or different? Why?