Question

vertically stretched by a factor of 2, then translated
4 units left and 1 unit down

Answer 1

A vertical stretch of scale factor 2, followed by a translation of 4 units left and 1 unit down is written as:

g(x) = 2*f(x + 4) - 1

How to write the given transformation?

For a general function f(x), a vertical stretch of scale factor K is written as:

g(x) = K*f(x).

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

• If N is positive, the shift is to the left.
• If N is negative, the shift is to the right.

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

• If N is positive, the shift is upwards.
• If N is negative, the shift is downwards.

So, if we start with a function f(x) and we stretch it vertically with a scale factor of 2, we get:

g(x) = 2*f(x)

Then we translate it 4 units left:

g(x) = 2*f(x + 4)

Then we translate 1 unit down:

g(x) = 2*f(x + 4) - 1

This is the equation for the transformation.

If you want to learn more about transformations, you can read:

https://brainly.com/question/4289712