Evaluate the limits of a graph with a jump discontinuity

The video tutorial covers the concept of end behavior in functions, focusing on how graphs behave as x approaches infinity or negative infinity. It then delves into piecewise functions, explaining how they can only equal one value and the significance of open and closed circles on graphs. The tutorial further explores limits, discussing how to approach them from the left and right, and the conditions under which a general limit does not exist. The importance of understanding left and right hand limits is emphasized, especially when they do not converge to the same value.

What happens to the graph of a function as x approaches infinity?

• It forms a loop.

• It continues to rise or fall indefinitely.

• It oscillates indefinitely.

• It approaches a finite value.

In a piecewise function, what does an open circle on the graph indicate?

• The function has a value at that point.

• The function does not have a value at that point.

• The function is undefined everywhere.

• The function has multiple values at that point.

What is the value of a piecewise function at x = -3 if there is a closed dot at that point?

• 3

• 0

• -2

• -3

What does it mean if the left-hand and right-hand limits of a function at a point are not equal?

• The function is continuous at that point.

• The general limit exists.

• The general limit does not exist.

• The function has a maximum at that point.

If the left-hand limit of a function exists but the right-hand limit does not, what can be concluded?

• The general limit exists.

• Both limits exist.

• Neither limit exists.

• Only the left-hand limit exists.