Write the rule that transforms p(x) into q(x), where q(x)=2p(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.

Step-by-step 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.

312312

step-by-step explanation: