Domain of Continuity
Interactive practice questions
A function $f\left(x\right)$f(x) is known to be continuous on the interval $\left(-\infty,\infty\right)$(−∞,∞).
Which of the following statements is true?
$f\left(x\right)$f(x) is discontinuous over all smaller intervals.
$f\left(x\right)$f(x) is continuous over all smaller intervals.
$f\left(x\right)$f(x) is continuous over some smaller intervals, and discontinuous over others.
Suppose the function is $f\left(x\right)=3x+8$f(x)=3x+8.
Which of the following statements are true? Select all that apply.
The function is discontinuous.
The function is continuous on $\left[4,6\right]$[4,6].
The function is continuous on $\left(-7,-1\right)$(−7,−1).
The function is continuous on $\left(0,\infty\right)$(0,∞).
Consider the function $f\left(x\right)=x^2+7x+10$f(x)=x2+7x+10 drawn below.
Consider the function $f\left(x\right)=4x^3-9x^2-2x+1$f(x)=4x3−9x2−2x+1.
Consider the function $f\left(x\right)=\left(x+7\right)\left(x-4\right)$f(x)=(x+7)(x−4) drawn below.