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How do you find the domain of #y= x^2-2#?

Answer 1

#x in RR#

#x^2-2# is a polynomial, which is defined for all real numbers.

This isn't something mysterious and earth-moving about polynomials, but any number, we can square it, and take it to whatever power for that matter and get a result. And we can subtract #2# from everything. Thus

#x inRR#

I hope this is useful.

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Answer 2

Genesis Allen

Domain: #{x|x " is " RR}# or #(-oo, oo)# in interval notation.

Range: #{y|y >=-2)# or #[-2, oo)#

This function is a quadratic #ax^2+bx+c# and all quadratics are parabolas their domain is not restricted and is all real numbers:

Domain: #{x|x " is " RR}# or #(-oo, oo)# in interval notation.

When the range is moved down 2 from the parent function, it becomes more interesting:

Range: #{y|y >=-2)# or #[-2, oo)#

x^2 -2 [-10, 10, -5, 5]} graph

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Answer 3

Ethan Adkins

To find the domain of ( y = x^2 - 2 ), you need to determine all possible values of ( x ) for which the function is defined. Since ( x^2 ) is defined for all real numbers, the only restriction comes from the term ( -2 ). Since there are no values of ( x ) that would make ( -2 ) undefined, the domain of ( y = x^2 - 2 ) is all real numbers, expressed as ( (-\infty, \infty) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.