How does the value of a affect the graph?

What affect does a positive value of a have on the graph?

Before, when a =1, each of the graphs went through the origin.

When a = 2, the graph no longer goes through the origin.

Below is a layered graph, showing when a=3, 4, 5, and 6.

What effect will a < 1 have on the graph?

From this layered graph we can draw several conclusions

A value of a that is a fraction less than 1 will

* have the same general shape as the typical "n leaf" rose.

* have 2 sets of petals.

* have outer petals that are shorter than those of a related graph

* have inner petals that are longer than those of a related graph

From this layered graph, we can see that the larger the denominator of a gets, the closer the outer and inner petals get to each other.

What happens when a is negative?

Nothing. The graph remains the same.

Click here to see a discussion of the graph when a = 0.

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