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

Question

Quizplus · Accepted Answer

The equation $y = (x + 1)^2 - 1$ is a quadratic function, which means its graph is a parabola. The domain of any quadratic function is all real numbers, $( - \infty , \infty )$, because you can plug any real number into the equation for $x$. The vertex of this parabola is at $(-1, -1)$, and since it opens upwards (the coefficient of $x^2$ is positive), the lowest value of $y$ is $-1$, making the range $[ - 1 , \infty )$.

Give the Domain and Range of the Relation y=(x+1)2−1y = ( x + 1 ) ^ { 2 } - 1y=(x+1)2−1

Give the Domain and Range of the Relation $y = ( x + 1 ) ^ { 2 } - 1$