What is the domain of y x 4?

Answer 1

Domain

Find the domain of y = x + 4

Domain simply means "what numbers can I use for X that give me an answer for Y?"

Domain is looking for the acceptable X values that work in the equation y = x +4

When looking for the domain, the rule of thumb is:

* No fraction? * No radical? (sqrt, cube root, etc) * No problems! If you don't see a fraction, or a radical, or both in your equation, the domain will always be "All real numbers". This means you can pick any number you want, plug it in for X, and you'll get an answer for Y.

If you do happen to have a fraction, radical (or both)...

----

Think about what "breaks" a fraction. What makes a fraction not work?

If you try to divide by 0, you get an error, or undefined on your calculator.

for example:

Find the domain of y = 1/(x -1)

1/x is a fraction, and we know having a 0 on the bottom would make it not work.

So what we do is say the domain is "all real numbers, except" and then find out what numbers break the function and fill that in later.

We set the bottom of the fraction = 0 to find out exactly which numbers will break it, and then solve for X.

x - 1= 0

x = 1

So we know that is we plug in a 1, it will break the fraction.

The domain of y = 1/(x - 1) is "All real numbers, except 1"

---- If you have a radical expression in your function:

example. y = sqrt(x+2)

We need to know what breaks a radical expression, what number(s) won't work?

Well, sqrt(0) is OK. it = 0.

sqrt(1) is ok, it = 1.

But what happens if I try sqrt(-1). Try it on your calculator.

You get an error message, right?

This is because you cannot take the root of a negative number. (at least, not yet)

This means, negative numbers break a function with a radical. So similarly to how we found the numbers that broke a fraction, we'll set what's inside the radical less than 0. Since negative numbers are less than 0.

x + 2 < 0 and solve for x

x < -2

So any number less than -2 will break my radical.

Your answer would be, "All real numbers >= -2" (since anything less than -2 is broken, but -2 is still OK)

To check:

y = sqrt( -2 + 2) = sqrt (0) = 0 - OK

y = sqrt( -3 + 2) = sqrt(-1) - breaks

I chose a number smaller than -2 to check.

---- If you get a problem where they use both fractions AND radicals, just use both techniques.

Ex: y = 1/sqrt(x + 2)

We know that having a 0 on the bottom of a fraction breaks it, but it OK for a radical to have a 0 in it. We need to combine both rules together.

Take the inside of the radical and set it less than(what breaks the radical) or equal to 0 (what breaks the fraction).

x + 2 <= 0

x <= -2

This means, any number less than or equal to -2 will break both the radical and the fraction.

This tells us that the domain has to be "All real numbers > -2" (not including -2 this time)