How do you find the domain and range of #y = 1/x+4#?

↳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
Pop Quiz Whiz
Aug 25, 2017

Domain: #x# does not equal #0#
Range: #y# does not equal #4#

Explanation:

To find the domain, ask "What can or can't #x# equal?"

In this case, #x# can equal anything but zero, since you can't divide by zero.

To find the range, we can simply say that since x can equal anything but zero, #1/x# equals everything but zero.

Therefore, the range is #y# does not equal 4.

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