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

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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.

1 Answer
Oct 22, 2017

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!