What is the domain and range of y = x ^2 - x + 5y=x2−x+5?

1 Answer
Trevor Ryan.
Feb 3, 2016

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]}

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