Old hsc question

No. Is there anything that x can't be or can you put any value in for x and get a value for y?
 
Yes it does. so you can put in x=0. Is there any number you can't put in for x and get a value for y?
 
You are not thinking!
Can you put in x=2 into 2x^2-8 and get a value for y?
Can you put in x=-2 into 2x^2-8 and get a value for y?
Can you put in x=78 into 2x^2-8 and get a value for y?
Can you put in x=-289.372 into 2x^2-8 and get a value for y?

Is there any number you can't put in for x and get a value for y?
 
AlonzoN said:
Yes.
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Good so there is no restriction on the domain. Remember the domain is the set of numbers that x can be. So here, x can be any real number. This can be written as -infinity symbol < x < infinity symbol.

Just to show you that is not always the domain. consider the function \(\displaystyle y=\frac{1}{x-2}\). What can't x be in this case?
 
AlonzoN said:
So unless it's in a fraction, x has to be between certain numbers?
Click to expand...
No not always. The domain in this case is all real numbers except 2. Because x can be anything else.

What about \(\displaystyle y=\sqrt{x}\) ?
 
Good! So the domain is everything except negative numbers ie 0<= x < infinity.

So to find what x can be (ie the domain), it is often useful to check out what x can't be first. Get it?
 
Yes!! Good. I find it useful to consider the graph to determine the range y= 2x^2 - 8 is a U parabola with it's TP on the y-axis at (0, -8), so there is a lower limit of -8, but no upper limit to what y can be.
 
Go and get some sleep!! Sleep is important for your brain to function best! Good night.
 
Thanks for that, I have another range question:

f(x) = √(x+1) for x >= 0

would the range be y >= 1?
 
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