Let

a$.$ Graph and label all endpoints of domain restrictions. Draw each graph on its domain restriction accurately with respect to concavity and label the function names. You will use this graph to demonstrate all definition work in $($b$)-($c$).$b$.$ Use the definition of limit existence to determine algebraically whether or not $\underset{x3}{lim}F(x)$ exists at $x=3.$ Proof format: Write vertically and use valid equal signs. Label the $2$ parts of the definition A and $B$ and choose $2$ colors to be transferred to the graph in part $($a$).$

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Substitute for $c,f$

Direct Substitution to compute the limit

Simplifyc. C$.$ Use the definition of limit existence to determine algebraically whether or not $\underset{x3}{lim}F(x)$ exists at $x=0.$ Proof format: Write vertically and use valid equal signs. Label the $2$ parts of the definition C and D and choose $2$ colors to be transferred to the graph in part $($a$).$

Quote

Substitute for $c,f$

Direct Substitution to compute the limit

Simplify

d$.$ Summary $($use appropriate interval notation$)$:

i$.$ Domain of $F$ :

ii$.$ Limit of $F$ exists: