[ppark9689]

is there any way to determine the domain and root of a function through a formula? or am i just not getting what i'm saying? That and inequalities, i don't this question:

Solve (x-2)(x+3)>0

[SccHarpGirl]

The domain of a function deals with the values that you put in - the numbers that you substitute for x. IE, if you have a function like y = squareroot(x), to find the domain you should think about what values you can substitute for x that logically make sense? Positive number? Yeah = y=squareroot(25) or any other positive number yields a good answer. Zero? Yes. y=squareroot(0) = 0. Negative numbers? Not unless you're working with complex numbers. y=squareroot(-25) doesn't have a real answer.

So the domain is x>=0.

I assume you mean roots, as in zeros, of a function?

For any general function, in order to get the roots, set y = 0 and solve for x.

For a quadratic formula, like:

y = x^2+1x-3

To find the zeros you can factor it:

y = (x-2)(x+3), and then set y = 0

0=(x-2)(x+3)

Which equals zero when x=2 or x=-3.

Inequalities are related. Let's look at your example:

(x-2)(x+3) > 0

so we saw earlier that the roots (zeros) are at 2 and -3.

We want to find numbers we can plug in for X that make that statement true.

Looking at (x-2) you see that this is going to be negative for X<2 and positive or zero elsewhere

Looking at (x+3) you see that this is going to be negative for X<-3 and positive or zero elsewhere.

Two positive numbers multiplied together = positive. So for instance, if we put any number greater than 2 into your equation, the inequality is satisfied: the answer is greater than zero.

A negative number and a positive number multiplied together = negative. So if we put a number between 2 and -3 into your equation, the answer is negative: inequality NOT satisfied.

A negative number and a negative number multiplied together = positive. So if we put a number less than -3 into that equation, the answer will be greater than zero and the inequality satisfied.

So there's our answer: X>2 and X<-3.

The slightly easier way, that I prefer, is to sketch the graph. You know that this is a parabola that opens upward, with roots at 2 and -3. From there, you can see that the graph will be negative (below the x-axis) between x=-3 and x=2, and everywhere else positive. So you conclude that the inequality is satisfied by X<-3 and X>2.

Hope this helps - I work as a math tutor so let me know if you have any other questions!

[ppark9689]

oic i guess i was thinking too hard about it, which i do almost all the time. Anyways i think i get it now. yeah Pre-cal is a huge hill to get over

[SccHarpGirl]

Awesome. Yes, Precal is, IMO, in some ways trickier than 1st semester calculus. Best of luck with it!

[tlj009]

Good explanation but y = x^2+1x-3 doesn't factor to y = (x-2)(x+3).

I think that you meant y = x^2+1x-6 = (x-2)(x+3).