How do you find the domain and range of # y=x^2+2#?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Bill Jorgensen
May 30, 2018

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

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

Explanation:

The domain of all quadratic functions is all real numbers, there are no restrictions on input:

#{x|x " is " RR}# or #(-oo,oo)#

The range of the parent function #y=x^2# is #0# to #oo# but your function has a shift of 2 up so the range is:

#{y|y>=2}# or #[2, oo)#

graph{x^2 +2 [-10.29, 9.71, -0.28, 9.72]}

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