What is the domain and range of the function y=x2−x+5?

1 Answer
marfre
Mar 10, 2018

Domain: (−∞,∞) or all reals
Range: [194,∞) or y≥194

Explanation:

Given: y=x2−x+5

The domain of an equation is usually (−∞,∞) or all reals unless there is a radical (square root) or a denominator (causes asymptotes or holes).

Since this equation is a quadratic (parabola), you would need to find the vertex. The vertex's y-value will be the minimum range or the maximum range if the equation is an inverted parabola (when the leading coefficient is negative).

If the equation is in the form: Ax2+Bx+C=0 you can find the vertex:

vertex: (−B2A,f(−B2A))

For the given equation: A=1,B=−1,C=5

−B2A=12

f(12)=(12)2−12+5

f(12)=14−24+204

f(12)=194=4.75

Domain: (−∞,∞) or all reals
Range: [194,∞) or y≥194

graph{x^2-x+5 [-25.66, 25.66, -12.82, 12.83]}

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