Mathematics for Teaching Algebra Making Sense of Power Function

## Making Sense of Power Function

The power function, $ax^n$, n = positive integral exponents is actually the ‘basic’ polynomial function.They are the first terms in the polynomial function.

With graphing utility, it is no longer as much fun to graph function. What has become more challenging is interpreting them. Here’s are a set of tasks you can ask your learners as review for function. You can give it as homework as well.

Consider the sets of power function in the diagrams below. Answer the following based on the diagram

1. What are the coordinates of the points of intersection?
2. Why do all the graphs intersect at those points?
3. When is $x^4 < x^2$?
4. When is $x^7 > x^3$?
5. Why is it that as the degree or exponent of x that defines the function increases, the graph becomes flatter for the interval -1<x<1 and steeper for x > 1 or x >-1 ?
6. Sketch the following in the graphs below: $t(x) = x^{10}$, $l(x)=x^9$
7. Why is it that power function with even exponents are in Quadrants I and II while power function with odd exponents are in Quadrants I and III? Why are they not in Quadrant IV?

What other questions can you pose based on the graphs above? Kindly use the comment section to suggest more questions. Thanks.