I'm in danger of failing this course for the second time, and my super-awesome teacher sent me this study guide. He said if I can get the problems on this guides, I'll be able to pass the test. The problem is that I need things explained to me a bajillion ways from sunday before I can understand them.

If anyone can run through even a few of these, really in depth, that would be just the most amazing thing ever. More important than the problems themselves, though, is the theory behind them. I'm basically incapable of abstract thinking (I'm exaggerating, but only slightly), and any help in understanding the reason behind the problems, or what they mean, that'd also be super-helpful.

Thanks for any help anyone can give.

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(a) If *y varies directly with **x*^{2} and *y = 256 when **x = 8, find an equation to represent this relationship.*

(b) Find *y if **x = 2.*

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(a) If *y is inversely proportional to 6* | x |

and y = 25

when x = 8,

find an equation to represent this relationship. (Round the constant of proportionality to three decimal places.)

(b) Find *y if x = 4.*

(Round your answer to two decimal places.)

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Use the graph to answer the questions.

Consider the graph of *f*(*x*).

(b) Estimate*f*(0).

(c) Estimate *x such that f(x) = 6.*

(Enter your answers as a comma-separated list.

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(b) Estimate *h*(9).

*h*(9) ≈

(c) Estimate *h*(−5).

*h*(−5) ≈

(d) Estimate *x* such that *h*(*x*) = −9.

(Enter your answers as a comma-separated list.)

*x* ≈

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Simplify the rational expression.5*b*^{3} − 4*b*^{2} − 9*b* |

4*b*^{2} |

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Simplify the rational expression.

*x*^{4}*y*^{2} − 6*x*^{3}*y*^{4} + 9*xy*^{3} |

------------------- (this is an over line, I was having trouble copying it, the other site is being weird)

6*x*

^{2}*y*

^{2 -- Multiplying rationals
x-6 6x-7
-- * --
x-7 6-x
-- } ÷