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
Noah G
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!

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