What is the domain and range of y=x^2-2?

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2 Answers
Jim G.
Jun 25, 2018

#x inRR,y in[-2,oo)#

Explanation:

#"y is defined for all real values of x"#

#"domain is "x inRR#

#(-oo,oo)larrcolor(blue)"in interval notation"#

#"the quadratic in the form "y=x^2+c#

#"has a minimum turning point at "(0,c)#

#y=x^2-2" is in this form with "c=-2#

#"range is "y in[-2,oo)#
graph{x^2-2 [-10, 10, -5, 5]}

MeneerNask
Jun 25, 2018

Since there no are fractions, roots, etc. involved the domain of #x# is not limited. #- oo < x< +oo#

Explanation:

The range of #y#:
#x^2# is always non-negative:
#x^2>=0->x^2-2>= -2#

So: #-2<=y<+oo#

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