Mark all TRUE statements.
A) $f(x)=|x-3|$
is continuous at x = 0.
B) $g(x)=\sqrt[3]{x}$
fails to be differentiable at x = 0.
C) $h(x)=|x+5|$
is not continuous at x = -5.
D) $r(x)=\frac{(x-3)^{2}}{(x-3)}$
is continuous for all values of x.
E)Any polynomial function is differentiable for all values of x.

Question

Mark all TRUE statements.
A) $f(x)=|x-3|$
 is continuous at x = 0.
B) $g(x)=\sqrt[3]{x}$
 fails to be differentiable at x = 0.
C) $h(x)=|x+5|$
 is not continuous at x = -5.
D) $r(x)=\frac{(x-3)^{2}}{(x-3)}$
 is continuous for all values of x.
E)Any polynomial function is differentiable for all values of x.

Quizplus · Accepted Answer

- A) The function $f(x)=|x-3|$ is continuous at $x=0$ because absolute value functions are continuous everywhere.- B) The function $g(x)=\sqrt[3]{x}$ is not differentiable at $x=0$ because its derivative, which involves a term with $x^{-2/3}$, is undefined at $x=0$.- E) Polynomial functions are differentiable everywhere because their derivatives, which are also polynomials, are defined for all values of $x$.

Mark All TRUE Statements f(x)=∣x−3∣f(x)=|x-3|f(x)=∣x−3∣ Is Continuous at X = 0 g(x)=x3g(x)=\sqrt[3]{x}g(x)=3x​

Mark All TRUE Statements $f(x)=|x-3|$ Is Continuous at X = 0 $g(x)=\sqrt[3]{x}$