Q2. The graph of y = f(x) is shown above. Find the following limits:

• (a)

• (b)

• (c)

• (d)

• (e)

• (f)

• (g)

• (h)

Background

Topic: Limits from Graphs

This question tests your ability to interpret limits using a graph, including one-sided limits, limits at infinity, and limits at points of discontinuity.

Key Terms and Concepts:

• Limit: The value a function approaches as the input approaches a certain point.

• One-sided limits: (from the left), (from the right).

• Limit at infinity: or describes end behavior.

• Discontinuity: A point where the function is not continuous (jump, removable, or infinite).

Step-by-Step Guidance

1. For each limit, identify the relevant portion of the graph. For example, for , observe the behavior of the function as moves far to the left.

2. For one-sided limits (like and ), look at the graph as approaches 4 from the left and right, respectively. Note any jumps or holes.

3. For , compare the left- and right-hand limits. If they are equal, the limit exists; if not, the limit does not exist.

4. For limits at points of discontinuity (like or ), check if the function approaches the same value from both sides, or if there is a jump or infinite discontinuity.

5. For , observe the graph near and see what value the function approaches.

Try solving on your own before revealing the answer!