## Function: Find a point on a graph by shifting

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
Alan51q
Posts: 5
Joined: Fri Feb 21, 2014 9:47 pm
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### Function: Find a point on a graph by shifting

Problem:

Suppose (-3,5) is a point on the graph of y=g(x),
What point is on the graph of y=g(3x+9)?

The book gives the answer as (-4,5), I'm assuming, by first subtracting 9 from -3 and then multiplying -12 by 1/3 to get the x coordinate. However, given the standard order of operations, I can't figure out why it shouldn't be (-10,5) by first multiplying 1/3 by -3 to get -1 and then subtracting -9 to get the x coordinate.

If anyone can help me understand why, I'd be thankful.

FWT
Posts: 153
Joined: Sat Feb 28, 2009 8:53 pm

### Re: Function: Find a point on a graph by shifting

Suppose (-3,5) is a point on the graph of y=g(x),
What point is on the graph of y=g(3x+9)?

The book gives the answer as (-4,5), I'm assuming, by first subtracting 9 from -3 and then multiplying -12 by 1/3 to get the x coordinate. However, given the standard order of operations, I can't figure out why it shouldn't be (-10,5) by first multiplying 1/3 by -3 to get -1 and then subtracting -9 to get the x coordinate.
They give some info on this here. I think you do it like this:

x = -3 is on the graph
3x+9 HAS TO equal -3 to be on the graph (because that's the ONLY x we KNOW is ok)
3x+9=-3
3x=-12
x=-4

Then plug in & get y=5 (because that's the y they gave us).

Alan51q
Posts: 5
Joined: Fri Feb 21, 2014 9:47 pm
Contact:

### Re: Function: Find a point on a graph by shifting

Suppose (-3,5) is a point on the graph of y=g(x),
What point is on the graph of y=g(3x+9)?

The book gives the answer as (-4,5), I'm assuming, by first subtracting 9 from -3 and then multiplying -12 by 1/3 to get the x coordinate. However, given the standard order of operations, I can't figure out why it shouldn't be (-10,5) by first multiplying 1/3 by -3 to get -1 and then subtracting -9 to get the x coordinate.
I think you do it like this:

x = -3 is on the graph
3x+9 HAS TO equal -3 to be on the graph (because that's the ONLY x we KNOW is ok)
3x+9=-3
3x=-12
x=-4

Then plug in & get y=5 (because that's the y they gave us).
Thanks for this. It makes total sense to solve it that way. I don't know why it wouldn't be explained that way in the book.