Write the domain and range of the function in interval notation.
-$$f ( x ) = x ^ { 2 } + 10 x + 6$$
A) Domain: $( 0 , \infty )$
Range: $( - \infty , - 19 ]$

B) Domain: $( - \infty , \infty )$
Range: $[ - 19 , \infty )$

C) Domain: $( - \infty , \infty )$
Range: $( - \infty , 6 ]$

D) Domain: $( - \infty , \infty )$
Range: $[ 6 , \infty )$

Question

Write the domain and range of the function in interval notation.
-$$f ( x ) = x ^ { 2 } + 10 x + 6$$
A) Domain: $( 0 , \infty )$
Range: $( - \infty , - 19 ]$

B) Domain: $( - \infty , \infty )$
Range: $[ - 19 , \infty )$

C) Domain: $( - \infty , \infty )$
Range: $( - \infty , 6 ]$

D) Domain: $( - \infty , \infty )$
Range: $[ 6 , \infty )$

Quizplus · Accepted Answer

The domain of any quadratic function is $(- \infty , \infty)$ because you can input any real number. To find the range, complete the square to find the vertex form of the equation: $f(x) = (x+5)^2 - 19$, indicating the vertex is at $(-5, -19)$ and since the coefficient of $x^2$ is positive, the parabola opens upwards. This means the minimum value of the function is $-19$, so the range is $[ - 19 , \infty )$.

Write the Domain and Range of the Function in Interval f(x)=x2+10x+6f ( x ) = x ^ { 2 } + 10 x + 6f(x)=x2+10x+6

Write the Domain and Range of the Function in Interval $f ( x ) = x ^ { 2 } + 10 x + 6$