the graph of a function is given. use the graph to find the indicated limits and function values, or state…

Explanation:

Step1: Analyze left - hand limit as x→3⁻

As x approaches 3 from the left - hand side (x→3⁻), we look at the y - values of the function on the graph for x values less than 3 getting closer to 3. From the given answer for part a, we know lim_{x→3⁻}f(x)=2.

Step2: Analyze right - hand limit as x→3⁺

To find lim_{x→3⁺}f(x), we look at the y - values of the function on the graph for x values greater than 3 getting closer to 3. Without seeing the actual graph, we assume we follow the same process of observing the trend of the function values. If the graph approaches a single y - value as x approaches 3 from the right, we can determine the limit. If the left - hand limit and right - hand limit are equal, then lim_{x→3}f(x) exists and is equal to that common value. If they are not equal, lim_{x→3}f(x) does not exist.

Step3: Find f(3)

To find f(3), we look at the y - value of the function at the point x = 3 on the graph. If there is a closed - circle at x = 3, that y - value is f(3). If there is an open - circle or a break at x = 3, we need to determine if the function is defined at that point based on the context of the graph.

Step4: Analyze limits as x→3.5⁻, x→3.5⁺ and x→3.5

For lim_{x→3.5⁻}f(x), we look at the y - values of the function for x values less than 3.5 getting closer to 3.5. For lim_{x→3.5⁺}f(x), we look at the y - values of the function for x values greater than 3.5 getting closer to 3.5. If lim_{x→3.5⁻}f(x)=lim_{x→3.5⁺}f(x), then lim_{x→3.5}f(x) exists and is equal to that common value.

Step5: Find f(3.5)

We look at the y - value of the function at the point x = 3.5 on the graph to find f(3.5).

Since we don't have the actual graph to complete the calculations for parts b - h, we'll just focus on the given part a and start part b. For part b: We need to look at the graph to see the trend of the function as x approaches 3 from the right. If the graph approaches a y - value as x gets closer to 3 from values greater than 3, we can determine the limit. Without the graph, we can't give a numerical answer. But if the graph is continuous at x = 3, then lim_{x→3⁺}f(x) will be equal to lim_{x→3⁻}f(x)=2. If there is a break or jump at x = 3, we need to observe the right - hand behavior.

Answer:

b. Without seeing the graph, we can't determine the value. If the function is continuous at x = 3, then lim_{x→3⁺}f(x)=2. If not, we need to analyze the right - hand side of the graph near x = 3. If the left - hand and right - hand limits are not equal, the answer is B. The limit does not exist.