Answer: - A horizontal shift of 3 units to the left.
- A vertical dilation of factor 2.
- A vertical shift of 6 units down.
Explanation:
Here we have 3 transformations:
I will start giving general cases for each transformation:
Horizontal shift.
When we have a function f(x), an horizontal shift to the right of N units (N positive) is written as:
g(x) = f(x - N)
So in our case, we have a shift to the LEFT of 3 units.
Vertical dilation/contraction.
A vertical dilation/contraction of factor A, is written as:
g(x) = A*f(x)
if A > 1, this is a dilation, if A < 1, this is a contraction.
In the case of our problem, we have A = 2.
Vertical shift:
A vertical shift is written as:
g(x) = f(x) + N.
If N is positive, we have a shift of N units up, if N is negative, we have a shift of N units down.
in this case, N = -6.
Then the transformations are:
q(x) = 2*p(x -(-3)) - 6
- A horizontal shift of 3 units to the left.
- A vertical dilation of factor 2.
- A vertical shift of 6 units down.