Find numbers a and b, or k, so that f is continuous at every point.
-$f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } , & \text { if } x \leq 4 \ k x , & \text { if } x 4 \end{array} \right.$
A) $k = 16$
B) $\mathrm { k } = \frac { 1 } { 4 }$
C) $\mathrm { k } = 4$
D) Impossible

Question

Find numbers a and b, or k, so that f is continuous at every point.
-$f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } , & \text { if } x \leq 4 \ k x , & \text { if } x > 4 \end{array} \right.$
A) $k = 16$
B) $\mathrm { k } = \frac { 1 } { 4 }$
C) $\mathrm { k } = 4$
D) Impossible

Quizplus · Accepted Answer

For continuity at $x=4$, we must have $\lim_{x	o 4^-}f(x)=\lim_{x	o 4^+}f(x)=f(4)$. This gives us $16=4k$, so $k=4$. Since the function is defined piecewise and the two pieces match up at $x=4$, the function is continuous everywhere.

Find Numbers a and B, or K, So That F f(x)={x2, if x≤4kx, if x>4f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } , & \text { if } x \leq 4 \\ k x , & \text { if } x > 4 \end{array} \right.f(x)={x2,kx,​ if x≤4 if x>4​

Find Numbers a and B, or K, So That F $f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } , & \text { if } x \leq 4 \\ k x , & \text { if } x > 4 \end{array} \right.$