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

Question

Quizplus · Accepted Answer

The domain of any quadratic function is all real numbers, $( - \infty , \infty )$, because you can plug any real number into the function for $x$. The range is $[ 5 , \infty )$ because the vertex of this parabola is at $(5, 5)$, and since the coefficient of the squared term is positive, the parabola opens upwards, making the minimum value of $y$ equal to 5.

Give the Domain and Range of the Relation y=(x−5)2+5y = ( x - 5 ) ^ { 2 } + 5y=(x−5)2+5

Give the Domain and Range of the Relation $y = ( x - 5 ) ^ { 2 } + 5$