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

enter image source here

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!

Related questions
Impact of this question
3951 views around the world
You can reuse this answer
Creative Commons License