Question

For what value or p will the function be continuous . Btw it’s number 5 not 6

Answer 1

SOLUTION

Looking at the piecewise function, what will make p continuous is the value of x common to both, looking at it, from the range of values

$\begin{gathered} -7\leq x\leq-1 \\ -1-1 is common to both. So we will substitute -1 for x into the equations, equate them and solve for p, we have [tex]\begin{gathered} x^2+4x-1 \\ (-1)^2+4(-1)-1 \\ 1-4-1=-4 \end{gathered}$

and

$\begin{gathered} -3x+p \\ -3(-1)+p \\ 3+p \end{gathered}$

equating we have

$\begin{gathered} -4=3+p \\ -4-3=p \\ -7=p \\ p=-7 \end{gathered}$

Hence the answer is -7