Find the constant a such that the function $f ( x ) = \left\{ \begin{array} { l l }
6 , & x \leq - 5 \
a x + b , & - 5

Question

Find the constant a such that the function $f ( x ) = \left\{ \begin{array} { l l } 
6 , & x \leq - 5 \
a x + b , & - 5 < x < 1 \
- 6 , & x \geq 1
\end{array} \right.$
is continuous on the entire real line.
A) $a = 2 , b = 0$
B) $a = 2 , b = - 4$
C) $a = - 2 , b = - 4$
D) $a = - 2 , b = 4$
E) $a = 2 , b = 4$

Quizplus · Accepted Answer

For the function to be continuous, the value of the function at $x = -5$ and $x = 1$ from the piecewise parts must match the constant values given for those intervals. At $x = -5$, $f(x) = 6$, so $a(-5) + b = 6$. At $x = 1$, $f(x) = -6$, so $a(1) + b = -6$. Solving these equations simultaneously gives $a = -2$ and $b = -4$.

Find the Constant a Such That the Function f(x)={6,x≤−5ax+b,−5<x<1−6,x≥1f ( x ) = \left\{ \begin{array} { l l } 6 , & x \leq - 5 \\a x + b , & - 5 < x < 1 \\- 6 , & x \geq 1\end{array} \right.f(x)=⎩⎨⎧​6,ax+b,−6,​x≤−5−5<x<1x≥1​

Find the Constant a Such That the Function $f ( x ) = \left\{ \begin{array} { l l } 6 , & x \leq - 5 \\a x + b , & - 5 < x < 1 \\- 6 , & x \geq 1\end{array} \right.$