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Dope Dealer
09-14-2003, 06:32 PM
Hey Guys. I took this course a couple months ago and got a 50, so I am retaking it. I just had a question about transformations.

Here it is:

What points do the graphs of Y=x²-3x and Y=3x-x² have in common? Explain.

OK, so I rearranged them so they look like this:

Y=x²-3x
Y=-x²+3x

Now I figuired out that equation 2 is a reflection of equation 1 on the X-Axis and it looks like the attatched image. Now, what is the reasoning behind the question that they share the same X's (Zero's).

On the diagram, I highlighted where the 2 graphs share the same points, but I don't know how to explain the reasoning behind it.

lammer
09-14-2003, 06:37 PM
because they are the same thing
- is one side
+ is the other
they are both x2 3x.

nickopolis
09-14-2003, 06:41 PM
I took math in french so i'm not sure on the english terms. I'lltry my best and i think this is right. The second equation Y=-x^2-3x is simply the first equation that has been "flipped"? about the x-axis and translated vertically by three units in the opposite direction of the first. Since it has not been "stretched"? or "translated" the zeros would not change. (it makes sense in my head been a while since i've had to explain math)

hope this helps ans isn't wrong :D

Dope Dealer
09-14-2003, 06:45 PM
Ahh, that makes more sense Nickopolis. Thanks. This book asks for very specific answers and it's probably about 5 years old as they still refer to inverse as f(y) instead of f -1 (superscript) (x).

I just wasn't sure if it had to be in specific terms (ie - Y=x²-3x is a vertical reflection of Y=-x²+3x in respect to the X-Axis blah blah).

Can anyone confirm Nick's answer? Looks right to me, but just making sure.

Dope Dealer
09-14-2003, 06:54 PM
Also, can someone give me a description of what each on entails:

y = f(x)
y = -f(x)
y = f(-x)
x = f(y)

I know the first one is the normal equation and the last is the inverse. What are the other two though? Y turns into the opposite in the (y =-f(x)) and x turns to the opposite in (y = f(-x))?

DUBBED
09-14-2003, 08:23 PM
Originally posted by nickopolis
I took math in french so i'm not sure on the english terms. I'lltry my best and i think this is right. The second equation Y=-x^2-3x is simply the first equation that has been &quot;flipped&quot;? about the x-axis and translated vertically by three units in the opposite direction of the first. Since it has not been &quot;stretched&quot;? or &quot;translated&quot; the zeros would not change. (it makes sense in my head been a while since i've had to explain math)

hope this helps ans isn't wrong :D

just so you know the graphs are mirrored accross the x-axis, there was no translation...

Team_Mclaren
09-14-2003, 08:46 PM
Originally posted by Dope Dealer
Also, can someone give me a description of what each on entails:

y = f(x)
y = -f(x)
y = f(-x)
x = f(y)

I know the first one is the normal equation and the last is the inverse. What are the other two though? Y turns into the opposite in the (y =-f(x)) and x turns to the opposite in (y = f(-x))?

Evan your a dumbas!!!!!

y=-f(x) is reflected on the x-axis. your new pointe will be (x, -y)
y= f(-x) is reflected on the y-axis. Your new points are (-x, y)
the last one x= f(y) is reflected on the y=x line. new points are
(y,x). so basicly x and y switch points!!
:thumbsup:

TheXplosion
09-14-2003, 10:17 PM
iam taking this right now in my math class i knwo everything about the functions your talking about but i dont knwo what you want/looking for. Be specific on what your looking for and ill tell you.

kaput
09-14-2003, 10:29 PM
.

lammer
09-15-2003, 12:10 AM
Originally posted by Team_Mclaren

Evan your a dumbas!!!!!

thhis might be the only thing making sense here. haha jk evan.

Dope Dealer
09-15-2003, 12:15 AM
Originally posted by kaput
What points do they have in common sounds like it's asking for the intercept so just set one equal to the other, get a quadratic equation and find the roots, those points will be common to both equations.

Can someone tell me how to do this? :rofl:

Thanks :)

TheXplosion
09-15-2003, 06:56 AM
to find the roots of a quadratic function you have to factor it, do you knwo how.

2 numbers that add to the middle number and 2 numbers to mulitply to the outside number.

then you should know where to go from there, this form of question is 20 pure.

o ya the points that you highlighted in your pic there called invareant (sp) points, their the poitns that dont move between a transformation of 2 graphs.

Dope Dealer
09-15-2003, 05:02 PM
Originally posted by TheXplosion
to find the roots of a quadratic function you have to factor it, do you knwo how.

2 numbers that add to the middle number and 2 numbers to mulitply to the outside number.

then you should know where to go from there, this form of question is 20 pure.

o ya the points that you highlighted in your pic there called invareant (sp) points, their the poitns that dont move between a transformation of 2 graphs.

Awesome. That's all I needed to know. Thanks!

TheXplosion
09-15-2003, 06:44 PM
np prob, i like math so ask away anyone and ill try my best.

Thx