What is the domain and range of #y = x ^2 - 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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