I am in College Algebra. We are going over Graphing Techniques. I'm pretty sure I understand it, but my teacher is confusing me (and barely speaks English, so it's tough asking questions). Anyways, the problem given is . . .
f(x) = (x-1)3 +2
and we are supposed to show variations of this problem using what we know about shifting, stretching, reflecting, etc.
The directions tell us to start with the basic form of the problem, in this case being x^3
My question is that my teacher tells us (and expects on the test) to show and graph the different variations of this equation. Such as
y2= x3 + 2
y3= (x-1)3 + 2
First off, I don't understand why we are supposed to do this, and my proficiency in math is primarily based on understanding the why.
Secondly, the book does not provide any information as how to do this. In fact, the only answer provided to this problem is the graph of (x-1)3 + 2 and nothing else. My textbook is Sullivan Algebra8 along with MyMathLab.
Other problems and the answers expected by my teacher. Again, answers in the book only provide graphs of the original question.
f(x) = (square root of)(x-2)
y1= (sq. rt)x
y2= (sq rt)(x-2)
f(x) = (sq rt)(-x) - 2
y1= (sq rt)x
y2= (sq rt)(x) - 2
y3=(sq rt)(-x) - 2
f(x)= -(x+1)3 - 1
y4= -(x+1)3 - 1
The Attempt at a Solution
In pretty much guessing, I got most of these right. But I still don't understand why I got them right. And I even moreso don't understand why the book is not showing any of this . . .
Any help would be great. The test is Friday.