Did I get it wrong? (transformation problem)

[dontdisturbmycircles]

Homework Statement

I just got back from writing my grade 12 math final and I figure I did really well. There was only one question that stumped me, and it was freaking stupid, too. So the problem was this:

There was a picture of y=x^{3} and the points P(2,8) was labelled. The question was where does the point P go if the graph is expanded horizontally by a factor of 3 about the line x=4... What the hell did they mean? I thought they meant that you first shift the graph over 4 places to x=4 and then you would apply the transformation, the point would end up being Q(10,8) but that wasn't even on there.

Here were my choices...

A.(8,8)
B.(14/3,8) (I think)
C.(10/3,8)
D.(-2,8)

I ruled out D pretty quickly and went with A... but it didn't make any sense. Did I get it wrong?

Pretty sad the the only question that stumped me was a transformation question...

Homework Equations

The Attempt at a Solution

 

[dontdisturbmycircles]

Woops, I meant you would apply the transformation and then shift it over, wrong way around. But anyways, both methods were fruitless.

 

[HallsofIvy]

Homework Statement

I just got back from writing my grade 12 math final and I figure I did really well. There was only one question that stumped me, and it was freaking stupid, too. So the problem was this:

There was a picture of y=x^{3} and the points P(2,8) was labelled. The question was where does the point P go if the graph is expanded horizontally by a factor of 3 about the line x=4... What the hell did they mean? I thought they meant that you first shift the graph over 4 places to x=4 and then you would apply the transformation, the point would end up being Q(10,8) but that wasn't even on there.

I would interpret that to mean that the point's distance from x= 4 is multiplied by 3- if x is larger than 4, then it moves to the right 3 times that distance. If x is less than 4, then it moves to the left 3 times that distance.

In this example, 2< 4 and the distance from 2 to 4 is 4-2= 2. (2, 8) is transformed to a point with x< 4 and 4- x= 3(2)= 6 so x= 4- 6= -2. Since the change is only horizontal, y does not change.
(2, 8) is transformed to (-2, 8)

Here were my choices...

A.(8,8)
B.(14/3,8) (I think)
C.(10/3,8)
D.(-2,8)

I ruled out D pretty quickly and went with A... but it didn't make any sense. Did I get it wrong?

Pretty sad the the only question that stumped me was a transformation question...

How did you rule out D "pretty quickly"?

 

[dontdisturbmycircles]

That sounds like a good interpretation. Definitely makes sense to me now that I think about it. I figured that no positive stretch is going to result in a positive point moving to the left... But I was wrong!

Thankyou for clearing that up, I understand the concept now.