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The graph of a function is shown at the right. Use the graph to evaluate the following limits.

  1. The limit does not exist, but .

  2. A limit is a predicted value (which sometimes differs from the actual function value). The prediction must agree from the left and the right.

  3. What is the prediction from the left?

  4. What is the prediction from the right?

  5. Most of the time, the limit and the function value agree.

  6. and will reveal the equation of a horizontal asymptote, if there is one.

  7. Where (if anywhere) does the derivative of not exist?

    Look for cusps, endpoints, jumps, holes, and vertical asymptotes.

Piecewise curves, with dashed vertical line at x = negative 1, as asymptote, left curve starting at (negative 2, comma 3),continuing to infinity, center curve coming from infinity stopping at open point (2, comma 2), right curve starting at open point (2, comma negative 2), turning at (5, comma 2), changing from concave up to concave down at (4, comma 1) & from concave down to concave up at (7, comma 1), continuing to the right above the x axis, & a closed point at (2, comma negative 1).