Determine the domain and the range of the function.
-$f ( x ) = x ^ { 2 } + 6 x + 5$
A) domain: range: {x|x ≥ 3}
B) domain: all real numbers range: {y|y ≥ -4} range: {y|y ≥ 4}
C) domain: range: {x|x ≥ 3}.
D) domain: all real numbers range: {y|y ≥ 4} range: {y|y ≥ -4}

Question

Quizplus · Accepted Answer

The domain of a quadratic function is all real numbers. The range can be found by completing the square or using the vertex formula. The given function $f(x) = x^2 + 6x + 5$ can be rewritten in vertex form to find the minimum value (which determines the range for a parabola that opens upwards). Completing the square or using the vertex formula, we find the vertex to be at $(-3, -4)$, indicating the range is $y \geq -4$.

Determine the Domain and the Range of the Function f(x)=x2+6x+5f ( x ) = x ^ { 2 } + 6 x + 5f(x)=x2+6x+5

Determine the Domain and the Range of the Function $f ( x ) = x ^ { 2 } + 6 x + 5$