# Unit 3 parent functions and transformations homework 1

### Question:

How can a function transform in four different ways?

### Answer:

A cubic function with the form y = a (x h) + k is different from y = x, where a, h, and k are all in R and an is less than 0. In this form, the value of a shows the scale factor for dilation, and a reflection happens if an is less than zero. If an is greater than zero, it moves to the right by h units and up by k units. The graph of a cubic function always has one point where the line goes in a different direction. As two critical points, it could have a local minimum and a local maximum. If it doesn’t, we say that a cubic function is monotonic. A cubic function has a graph that is symmetric around the point where it changes direction. This means that if you turn this point a half turn, it doesn’t change.