4. Let’s see if I can explain this in words. This is not the same as just finding f (3). As you can see, there is no point there. To find the limit of f ( x ) as x approaches 3, put your finger over the picture at x = 3. With that open circle hidden, ask yourself, “what does it look like f(3) might be if you had to guess at it?” You would let your eyes follow the line right on up there really close to the hidden part. What y value is it getting closer and closer to? If you had the equation to work with, you could plug in values for x like 2.5, 2.8, 2.9, 2.99, and see what the y-values are “approaching.”

5. Put your finger over the graph at x = -2, and pretend like you don’t know what it is. Look at BOTH sides of your finger. The graph on either side of your finger need to be pointing at the same y value. In this case, the two sides of the finger seem to agree.

6. Compare: f(x) and g(x)

7. What if the two sides don’t agree? After you give it the finger: ANSWER:_________________________________.

9. Make sure you can do all the suggested problems. You might need to be reminded about more algebra stuff [order of operations, negative exponents, rational exponents, radicals, etc.]

10. D. How to find a limit by simplifying There is a problem with “direct substitution” here!

14. A limit only exists if the limit from the left and the limit from the right are equal to each other.

16. You try this one:

27. Jumps are discontinuities too: This one has a discontinuity at x = 3.

28. Vertical asymptotes are discontinuities. This one has a discontinuity at x = 2.