Find numbers a and b, or k, so that f is continuous at every point.
-$f ( x ) = \left\{ \begin{array} { l l } 10 x + 8 , & \text { if } x

Question

Find numbers a and b, or k, so that f is continuous at every point.
-$f ( x ) = \left\{ \begin{array} { l l } 10 x + 8 , & \text { if } x < - 7 \ k x + 2 , & \text { if } x \geq - 7 \end{array} \right.$
A) $\mathrm { k } = \frac { 64 } { 7 }$
B) $\mathrm { k } = \frac { 2 } { 7 }$
C) $k = 16$
D) $k = - \frac { 2 } { 7 }$

Quizplus · Accepted Answer

For $f(x)$ to be continuous at every point, the two expressions must equal each other at $x = -7$. Setting $10(-7) + 8 = k(-7) + 2$, we get $-70 + 8 = -7k + 2$, which simplifies to $-62 = -7k + 2$. Solving for $k$, we get $k = \frac{64}{7}$.

Find Numbers a and B, or K, So That F f(x)={10x+8, if x<−7kx+2, if x≥−7f ( x ) = \left\{ \begin{array} { l l } 10 x + 8 , & \text { if } x < - 7 \\ k x + 2 , & \text { if } x \geq - 7 \end{array} \right.f(x)={10x+8,kx+2,​ if x<−7 if x≥−7​

Find Numbers a and B, or K, So That F $f ( x ) = \left\{ \begin{array} { l l } 10 x + 8 , & \text { if } x < - 7 \\ k x + 2 , & \text { if } x \geq - 7 \end{array} \right.$