Need help with transformations of functions

[Intr3pid]

hi everyone

I have trouble recognizing expansions/compressions, and not knowing how draw graphs of recipricol transformations (of functions). can someone explain to me how to "do" them? or recommend a site that has a tutorial about it?

thanks in advance.

 

[Concorde]

Ok, there are two types of expansion/compression. First, you have expansion/compressiion that affects your y value. Generally, you recognize this when you have a number times the x variable after some kind of operation is being performed (2x^2, 2*(x)^(1/2), etc). You simply take the original Y value and multiply it by this number to get your new Y value. If this number is greater than 1 you are "stretching" and if it's between 0 and 1 then you are "compressing" it.

Next, you have expansion/compression that can affect your x value. This will occur when the X is being multipled by some number BEFORE the operation is taking place like (2x)^2, (2x)^1/2, etc. However, the effect is a bit diffrent from what happened with the Y value a min ago. Whenever the number being multiplied by x is greater than 1, you take that numbers reciprocal and multiply it by the original x value to obtain the new x value. If it's less than 1 (IE a fraction), you will multiply by the reciprocal of the fraction (which is usually a whole number, since most problems of this type are 1/3, 1,4, etc)

Now for reflections. You will have a reflection of a number over the x-axis (just take the y value and change the sign) if x is being multiplied by something negative if the multiplication is occurring AFTER the operation (-x^2, -(x)^(1/2), etc).

You will have a Y axis reflection (change the signs of the x values) if the negative number is being multiplied BEFORE the operation (-x)^(2), (-x)^(1/3), etc.

I hope that wasn't too confusing and this helps you.

 

[Concorde]

Just a few pratical examples for you

Vertical stretching: 2x^2
Vertical compression: (1/2)x^2

Horizontal stretching: (1/2x)^2
Horizontal compression: (2x)^2

X axis reflection: -x^2
Y axis reflection: (-x)^(1/2)

So in F(x)=-2(x+5)^(2)+3 for example you would graph x^2 then:
Move the graph left 5 units, multiply your x value by 2, change the x value's sign to obtain a reflection, then move it up 3 units.

 

[Intr3pid]

what about recipricol transformations?

 

[Concorde]

I'd just graph those in the traditional method finding points, intercepts, end behavior, etc, since you could end up with asymptotes and stuff that the transformations would neglect. That is, if the reciprocal of your original function contains fractions. If the reciprocal of the orgininal happens to end up being something nonfractional and you have a parent graph from which to use to transform it, then the same rules apply as what I listed above.

 

[Intr3pid]

I'd just graph those in the traditional method finding points, intercepts, end behavior, etc, since you could end up with asymptotes and stuff that the transformations would neglect. That is, if the reciprocal of your original function contains fractions. If the reciprocal of the orgininal happens to end up being something nonfractional and you have a parent graph from which to use to transform it, then the same rules apply as what I listed above.

no idea wat u're saying about recipricols.