# Thread: Help on Pre-Calculus Review

1. ## Help on Pre-Calculus Review

Hi this is my first day of taking Calculus and I haven't taken any math classes since Pre-Calculus which was 2 years ago. I would like some help on solving these problems so any help would be very appreciated. Thanks in advanced!

I know you can solve them using graphing calculators but I need help on how to find the Domain and Range of these problems without using a Calculator...

1) y = ln(Xsquared - X - 6)

2) y = sin(3X - pie)

3) y = tan(2X)

Find the difference in quotient, (f(X + H) - f(X)) / H, for f(X) = Xsquared - 2X and g(X) = (2X)/(X-1)

I forgot how to do these kind of problems and they confuse me so much so any help would be appreciated...

2. Originally Posted by alienware

I know you can solve them using graphing calculators but I need help on how to find the Domain and Range of these problems without using a Calculator...

1) y = ln(Xsquared - X - 6)

the domain will be where $\displaystyle x^2-x-6>0$ as this is where the $\displaystyle \ln$ function is defined

Originally Posted by alienware

2) y = sin(3X - pie)
Can you think of any values for x that this function won't accept?

Originally Posted by alienware

3) y = tan(2X)
Do you know where $\displaystyle \tan$ has asymptotes?

Originally Posted by alienware

Find the difference in quotient, (f(X + H) - f(X)) / H, for f(X) = Xsquared - 2X and g(X) = (2X)/(X-1)
The answer is in front of you

$\displaystyle f(x) = x^2-2x \implies f(x+h) = (x+h)^2-2(x+h)$

Now substitute these into

$\displaystyle \frac{f(x+h)-f(x)}{h}$