Find numbers a and b, or k, so that f is continuous at every point.
- $f ( x ) = \left\{ \begin{array} { l l } 1 , & x < 2 \\a x + b , & 2 \leq x \leq 3 \\- 1 , & x > 3\end{array} \right.$

Question

Find numbers a and b, or k, so that f is continuous at every point.
-$f ( x ) = \left\{ \begin{array} { l l } 
1 , & x < 2 \
a x + b , & 2 \leq x \leq 3 \
- 1 , & x > 3
\end{array} \right.$
A) a = 1, b = -1
B) a = -2, b = -7
C) a = -2, b = 5
D) Impossible

Quizplus · Accepted Answer

To ensure continuity, the function values must match at the transition points x = 2 and x = 3. Solving for a and b using these conditions, we find a = -2 and b = 5.

Find Numbers a and B, or K, So That F f(x)={1,x<2ax+b,2≤x≤3−1,x>3f ( x ) = \left\{ \begin{array} { l l } 1 , & x < 2 \\a x + b , & 2 \leq x \leq 3 \\- 1 , & x > 3\end{array} \right.f(x)=⎩⎨⎧​1,ax+b,−1,​x<22≤x≤3x>3​

Find Numbers a and B, or K, So That F $f ( x ) = \left\{ \begin{array} { l l } 1 , & x < 2 \\a x + b , & 2 \leq x \leq 3 \\- 1 , & x > 3\end{array} \right.$