First, make the table so you can sketch the graph:
x | y
5 | 20
4 | 9 x² - 5 ; x > 3
3 | 4 (open dot) ⇒ from the right
3 | 5 5 ; x = 3 ⇒ at x = 3
3 | 2 (open dot) ⇒ from the left
2 | 4 -2x + 8 ; x < 3
1 | 6
Next, look at the graph (or table) to find the limits:
lim 3⁺ = 4 as x approaches 3 from the right, y approaches 4
lim 3⁻ = 2 as x approaches 3 from the left, y approaches 2
lim 3 = DNE lim 3⁺ ≠ lim 3⁻ so the limit does not exist
f(3) = 5 when x = 3, y = 5
f(x) is NOT continuous at x = 3 because lim 3 ≠ f(3)
