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

Answer 1

The function is a polunomial, so its domain is the whole set of real numbers. #D=RR#.

We must consult the formula in order to determine the range.

The graph of the function is a parabola. The coefficient of #x^2# is positive, so the parabola goes to #+oo# as the argument goes to #+-oo#, so the range is #R= < q;+oo)#, where #q# is the #y# coordinate of the vertex.

To calculateit we can first calculate #x# coordinate of the vertex (usually called #p#)

#p=(-b)/(2a)=1/2#

Now we can calculate #q# by substituting #p# to the function's formula:

#q=f(1/2)=(1/2)^2-(1/2)+5=4 3/4#

The range can now be written:

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Answer 2

Genesis Allen

The domain is all real numbers, and the range is y ≥ 4.

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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.