Explanation:
a. For any function, in order for a vertical stretch to happen, a must be greater than 1 so the answer to a is
a>1.
b. For b, the graph will compress when a is between 0 and 1 but not equal to both.
So the answer to. b is
0<a<1.
c.A vertical stretch happens when a>1, a horinzontal compression also happens when a>1, if you confused let me explain
Consider the graph above. Let say we have a quadratic function
Let that be the parent function, if we stretch the function, a must be greater than 1 as we established in a.
In the fist picture, let say a=2.7
The function is stretched in the vertical direction
Now, let say if we affect x.
Here, let a=2.7 we know have
The function is being compressed when a>1, so that means that
we stretched vertically or compressed horizontally when a>1. It depends on the location of a. If a is outside the parenthesis, we will stretch by a factor of a. If a is I side the parenthesis, we will compress by a factor of a.
d. A must be negative or a<0