Let
\[
f(x)=\left\{\begin{array}{ll}
-x+b, & \text { if } z<3 \\
5, & \text { if } z=3 \\
\frac{-x}{x-6}+0, & \text { if } z>3(\text { and } x \neq b)
\end{array}\right.
\]
(a) For what value(s) of \( b \) is \( f \) continuous at 3 ?
Answer: \( b= \) \( \square \)
(b) For what value(s) of ib does \( f \) have a removable discontinuity at 3 ?
Answer: \( b= \) \( \square \)
(c) For what value(s) of \( b \) does \( f \) have an iedirite discontinuity at 3 ?
Answer: \( b= \) \( \square \)
(d) For what value(s) of b does \( f \) have a jump discontinuity at 3 ?
Witte your answer in interval notation using "U* for union.
For example, \( (-1,1) \cup(2,3) \) is the set of all real numbers \( x \) so that \( -1<x<1 \) or \( 2<x \leq 3 \).
Answer: \( b \) is in the set \( \square \)
Hint: use a process of elimination to consider all of the possible behaviours that the function could have at \( x=3 \).
