maths help thread

[lolbox]

hey guys, would appreciate help with some of these questions (maths is definitely not my forte unfortunately)

- its pretty easy i think


The graph of the function f is obtained from the graph of y=1/x by the following transformations applied in the order given

a dilation by factor of 0.5 from the y-axis
a reflection in the y axis
a translation of 3 units parallel to the x axis
a translation of 1 unit parallel to the y axis


write down the rule for f and hence state the domain and range of f

[TrueTears]

(x,y) -> (0.5x,y) -> (-0.5x,y) -> ( -0.5x+3,y+1)

[for the last transformation i assume you mean in the positive direction.]

x' = -0.5x+3

y ' = y+1

(x'-3)/(-0.5) = x

y'-1=y

=> y'-1 = 1/((x'-3)/(-0.5))

[the.watchman]

Here's another way (sorry TT ):

1) Dilation by factor from the y-axis



2) Reflection in the y-axis



3) Translation three units right, one unit up (same assumption as TT)





SO

I think this way is a little quicker in determining the effect of transformations, although it is important to learn TT's way for more complex transformations.
All the best!

[Cthulhu]

Beating TrueTears at his own game? +1 for you sir!

[TrueTears]

assumption of y = f(x) is invalid

[the.watchman]

assumption of y = f(x) is invalid

Erm ... the question does say the transformed function is f ...

[TrueTears]

Let y = f(x) valid

[lolbox]

cheers
I've got a few more q's

(1) Let p(x) = (x^2 + a) (x + b) (x - c) where a, b and c are three distinct positive real numbers. What is the number of real solutions to the equation p(x) = 0

Not sure how to do this at all so instead of just saying the answer, I'd appreciate a bit of working out to guide me for future q's. thanks

[/0]

When solving quadratic equations, you are normally able to factor them, for example:

Now, either , OR , it's just the null factor theorem

With ,

OR OR

or or

However, since is a positive number, will be negative, and the square root of a negative number is not on the real number line, so is not a real solution.

So we have and , so 2.

[the.watchman]

http://vcenotes.com/forum/index.php/topic,23815.0.html

Although that was a bit of a mess