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Is the function graphed at right continuous at the following values of ? If not, explain which conditions of continuity fail. 


Dashed vertical line at x = 2;  ray starting at (negative 4, comma 0), extending left & up; semicircle, diameter endpoints at (negative 4, comma 0), & the origin, &, decreasing curve starting at open point (0, comma negative 2.5), opening down, continuing to negative infinity left of vertical line, & decreasing curve, coming from infinity right of vertical line, passing through the point (3, comma negative 1), extending to the right above, y = negative 2.

Look at your Math Notes for the three conditions of continuity.

Use the three conditions to test if the function is continuous at and .

Examine the graph at .

Condition 1:

Condition 2:

Therefore exists.

Condition 3:

The function is continuous at .