How do you find the domain and range for #y = x^2-5#?

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Answer 1 · 2016-07-03T06:11:01

the domain is #RR#, the range is #[-5, +oo)#

Since y is a polynomial, its domain is #RR#

Then you find x:

#x^2=y+5#

that has two solutions:

#x=+-sqrt(y+5)#

that are verified only if #y+5>=0#

or #y>=-5#

Then the range of y is #[-5, +oo)#

You also can see the domain and the range in the graphic:

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

the domain, on x-axis, is all along the line,
the range begin in the y-coordinate -5 and continues to #+oo#