Question

The graph of f(x) contains the point (3,-2). What corresponding point must be on the graph of g(x) = 2f(x) − 9 ?

Do we have to actually graph to get to the solution? I know that the graph is shifted right by 9 units and has a vertical compression of 2.

Answer 1

The answer is `(12, -4)`.

Explanation:

I will be using the official question (numbered #3).

The graph of `y= f(x)` can be written as

`y = af(b(x- c)) + d`

Where:

`•a` is the vertical stretch/compression
`•b` is the horizontal stretch/compression
`•c` is the horizontal transformation
`•d` is the vertical transformation

The formula `(m/b + c, an + d)` helps me remember the corresponding point after the transformations have been applied. In that formula `(m, n)` is our original point and `a, b, c and d` are our parameters.

In our question, we have `a = 2`, `b = 1`, `c = 9` and `d = 0`.

Applying the formula, we get:

`(3/1 +9, 2(-2) + 0) = (12, -4)`

As required. My tip is just memorize that formula. It will be of great help to you, trust me.

Hopefully this helps!