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Atomic Boo

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Heya, I once again return to this thread.. yay!

 

I'm doing my R.E. homework which I hate doing, and I'm fairly stuck on this statement and what to write;

 

C) Explain why Catholics believe evil and suffering exists.

 

Now, I know the basis, people were given free will by God, so they can do what they want, but I don't know how to elaborate on it, and any other points! Any help will be appreciated.

 

Thanks in advance

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Maths stuff again:

 

"Write down the gradient of the straight line and the intersection of the y axis"

 

5X+2Y=7

 

Well for the intersection, this is when X=0, therefore the X is taken out of the equation. Then it goes 2y=7, therefore y=3.5

 

 

Now this is embarassing, but I can't remeber how to work out the gradient from this. Its there on the tip of my tongue but I can't quite remember it. Someone put me out of my misery and answer him :D

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Well for the intersection, this is when X=0, therefore the X is taken out of the equation. Then it goes 2y=7, therefore y=3.5

 

 

Now this is embarassing, but I can't remeber how to work out the gradient from this. Its there on the tip of my tongue but I can't quite remember it. Someone put me out of my misery and answer him :D

 

Thanks :) it was more of a check really. I was positive i was wrong, but i got 3.5 aswell. For the gradient i got 2.5 (Being the 5 before the x devided by 2)

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Thanks :) it was more of a check really. I was positive i was wrong, but i got 3.5 aswell. For the gradient i got 2.5 (Being the 5 before the x devided by 2)

 

Ah, so all you do is rearrange it. Can't believe I thought there was something more complicated you had to do >_< Well no-one will want me to help again xD

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For the lines thing:

 

All straight lines can be rearranged into the form y = mx + c.

 

This is a useful form because m is the gradient of the line and c is the y intersect.

 

This stands to reason if you compare it with the line y = x: y = x is stretched in the y direction by m and translated by c in the y direction.

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Functions - Drawing graphs

 

I'm kinda stuck with these as I can't remember how to do them (duh).

 

Draw the graph of y =f(x) for the following functions. On the same diagran draw the graph of the inverse function f^-1 (x).

 

(a) f(x) = 3x + 2

 

(b) f(x) = x^3 - 3

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Functions - Drawing graphs

 

I'm kinda stuck with these as I can't remember how to do them (duh).

 

Draw the graph of y =f(x) for the following functions. On the same diagran draw the graph of the inverse function f^-1 (x).

 

(a) f(x) = 3x + 2

 

(b) f(x) = x^3 - 3

 

First of, there is an easy way to find the inverse of a function: change the f(x) to a y, then make all ys xs and all xs ys. Now rearrange for y and replace with f^-1(x). f^-1(x) should be a reflection of f(x) in the line y = x, so if this is indeed the case then you'll know that you're right.

 

(a) This follows y = mx + c, as I was talking about earlier, so it's a straight line with gradient 3 and y intercept 2.

 

For the inverse:

 

x = 3y + 2

 

y = x/3 - 2/3

 

f^-1(x) = x/3 - 2/3

 

So it is a straight line with gradient 1/3 and y intercept -2/3.

 

 

(b) This curve is a transformation of x^3, which is a curve with a single turning point (inflection on the origin) and a gradient which is always greater than 0. The -3 translates the curve by -3 in the y direction.

 

As for the inverse:

 

x = y^3 - 3

 

y = cuberoot(x + 3)

 

f^-1(x) = cuberoot(x + 3)

 

So this is the curve cuberoot(x) translated by -3 in the x direction. (note this funtion only has an inverse where x > -3)

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