How do you find the domain and range of y = x^2 - x + 5y=x2−x+5?

1 Answer
Daniel L.
Nov 17, 2017

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

To find the range we have to look at the formula.

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

Now we can write the range:

R=<4 3/4;+oo)

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