Find the domain and range of the function.
-$$y = ( x + 1 ) ^ { 2 } + 5$$
A) Domain: $( - \infty , \infty )$; Range: $[ 5 , \infty )$
B) Domain: $[ 5 , \infty )$; Range: $[ - \infty , 5 )$
C) Domain: $( - \infty , \infty )$; Range: $[ - 1 , \infty )$
D) Domain: $[ - 1 , \infty )$; Range: $[ - \infty , 1 )$

Question

Quizplus · Accepted Answer

The function $y = (x + 1)^2 + 5$ is a quadratic function, which means its graph is a parabola. Since $x$ can take any real value, the domain is all real numbers $(-\infty, \infty)$. The vertex of this parabola is at $(-1, 5)$, and since it opens upwards (the coefficient of $x^2$ is positive), the minimum value of $y$ is 5, making the range $[5, \infty)$.

Find the Domain and Range of the Function y=(x+1)2+5y = ( x + 1 ) ^ { 2 } + 5y=(x+1)2+5

Find the Domain and Range of the Function $y = ( x + 1 ) ^ { 2 } + 5$