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If they dont tell us about any restrictions. We can now assume that the the domain is going to be from negative infinity. All the way to infinity right like over there.

Theres no restrictions. So we can assume that however we have to look at kind of our embedded in restrictions. We know that if theres a variable in the denominator that cant make the denominator equal to zero.

And thats what i was trying to say in that i dont really like how actually i do so we cant make the denominator equal zero. So i have a variable in here.

I need to figure out what number then makes my denominator equal to zero. Well the easiest way to do that is to take out the denominator and just set it equal to zero. So i can find the value of x.

That does that so using our inverse operations. Form algebra. X.

Equals. Three halves.

So that means. When x. Is equal to three halves.

When x is equal to three halves that makes my denominator zero. So guess what three halves is not inside the domain. So we have our function our function goes all the way to infinity.

It can do whatever stuff it wants to do. But at three halves heres one heres two three apses like right here at three halves.

Theres either a hole or an asymptote. We dont know what it is right now were gonna learn about how to determine your asymptotes and holes later. But for right now you can just say this function continue is continuous.

Except it doesnt it doesnt include the value three apps and then it continues from there so its all real numbers. Except for that value okay. Now i want to show you guys how to write that in interval form.

Because it we wrote all real numbers as negative infinity to infinity. But in reality.

This is going from negative infinity to how far over does it go till. It has to stop two three apps then its dark back starts back up again from three half to infinity you guys kind of agree and it doesnt include three apps. Thats why its a parenthesis so to connect these we use the union symbol okay.

Yes. Its just me make telling you its like a made up graph. I mean i dont know what the graph looks like okay.

I mean. Its definitely a function. But we dont know what the graph looks like if probably something easy right.

Its not gonna be something crazy and actually lets go and take a look at the graph to make sure that makes sense. So we will be practicing this next class period. .

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