Find the domain and range of the function.
-$$y = ( x + 8 ) ^ { 2 } + 3$$
A) Domain: $[ 3 , \infty )$; Range: $[ - \infty , 3 )$
B) Domain: $( - \infty , \infty )$; Range: $[ - 8 , \infty )$
C) Domain: $[ - 8 , \infty )$; Range: $[ - \infty , 8 )$
D) Domain: $( - \infty , \infty )$; Range: $[ 3 , \infty )$

Question

Quizplus · Accepted Answer

The function $y = (x + 8)^2 + 3$ is a quadratic function, which means its graph is a parabola. Since the squared term is positive, the parabola opens upwards. The domain of any quadratic function in this form is all real numbers, $(-\infty, \infty)$, because you can plug any real number into $x$ and get a real number out for $y$. The vertex of this parabola is at $(-8, 3)$, which is its minimum point since it opens upwards. Therefore, the smallest value $y$ can be is 3, making the range $[3, \infty)$.

Find the Domain and Range of the Function y=(x+8)2+3y = ( x + 8 ) ^ { 2 } + 3y=(x+8)2+3

Find the Domain and Range of the Function $y = ( x + 8 ) ^ { 2 } + 3$