Describe the interval(s) on which the function $f ( x ) = \left\{ \begin{array} { l }
x ^ { 2 } - 100 ,\
10 x + 100,
\end{array} \right.$ $\begin{array} { l }
x \leq 0 \
x 0
\end{array}$ is continuous.
A) $( - \infty , 0 ]$ and $( 0 , \infty )$
B) $( - \infty , 0 )$ and $[ 0 , \infty )$
C) $( - \infty , 0 )$ and $( 0 , \infty )$
D) $( - \infty , \infty )$
E)none of these choices

Question

Describe the interval(s) on which the function $f ( x ) = \left\{ \begin{array} { l } 
x ^ { 2 } - 100 ,\
10 x + 100,
\end{array} \right.$ $\begin{array} { l } 
x \leq 0 \
x > 0
\end{array}$ is continuous.
A) $( - \infty , 0 ]$ and $( 0 , \infty )$
B) $( - \infty , 0 )$ and $[ 0 , \infty )$
C) $( - \infty , 0 )$ and $( 0 , \infty )$
D) $( - \infty , \infty )$
E)none of these choices

Quizplus · Accepted Answer

The function is continuous on the interval $( - \infty , 0 )$ because the first piece of the function is a polynomial, which is continuous on all real numbers. The function is also continuous on the interval $( 0 , \infty )$ because the second piece of the function is a polynomial, which is continuous on all real numbers. However, the function is not continuous at $x = 0$ because the two pieces of the function have different values at that point.

Describe the Interval(s) on Which the Function f(x)={x2−100,10x+100,f ( x ) = \left\{ \begin{array} { l } x ^ { 2 } - 100 ,\\10 x + 100,\end{array} \right.f(x)={x2−100,10x+100,​

Describe the Interval(s) on Which the Function $f ( x ) = \left\{ \begin{array} { l } x ^ { 2 } - 100 ,\\10 x + 100,\end{array} \right.$