Question

What is the domain and range of `y = x ^2 - x + 5`?

Answer 1

Domain = `RR`.
Range = `[4.75,oo)`

Explanation:

This is a 2nd degree quadratic equation so its graph is a parabola with arms going up since the coefficient of `x^2` is positive, and turning point (minimum value) occurring when `dy/dx=0`, that is when `2x-1=0`, whence `x=1/2`.
But `y(1/2)=4.75`.

Hence the domain is all allowed input x-values and is thus all real numbers `RR`.
The range is all allowed output y values and is hence all y-values bigger than or equal to `4.75`.

The plotted graph verifies this fact.

graph{x^2-x+5 [-13.52, 18.51, -1.63, 14.39]}