Find numbers a and b, or k, so that f is continuous at every point.
- $f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } , & x < - 4 \\a x + b , - 4 \leq x \leq 2 \\x + 2 , & x > 2\end{array} \right.$

Question

Find numbers a and b, or k, so that f is continuous at every point.
-$f ( x ) = \left\{ \begin{array} { l l } 
x ^ { 2 } , & x < - 4 \
a x + b , - 4 \leq x \leq 2 \
x + 2 , & x > 2
\end{array} \right.$
A) a = -2, b = -8
B) a = 2, b = 8
C) a = -2, b = 8
D) Impossible

Quizplus · Accepted Answer

For f to be continuous at -4 and 2, we need the two parts to agree at these points. So we need $a(-4)+b=(-4)^2$ and $a(2)+b=2+2$. Solving these gives $a = -2, b=8$. Therefore, the function becomes:
$$f(x)=\left\{\begin{array}{ll} x^2& x<-4\ -2x+8& -4\le x\le 2\ x+2& x>2 \end{array}ight.$$
This is a continuous function since each piece is continuous and the values at $-4$ and $2$ agree.

Find Numbers a and B, or K, So That F f(x)={x2,x<−4ax+b,−4≤x≤2x+2,x>2f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } , & x < - 4 \\a x + b , - 4 \leq x \leq 2 \\x + 2 , & x > 2\end{array} \right.f(x)=⎩⎨⎧​x2,ax+b,−4≤x≤2x+2,​x<−4x>2​

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