Pre calculus ! write the range of the function given in the graph in interval notion? i think the answer is b. write the domain of the function given in the graph in set builder notation. i think the answer is c. am i correct?

Question 1: C. (-4, 8]

With B, I think you assumed since there are two separate lines for the function, there must be two separate ranges. Additionally, you state that the left one has a range from -4 to 3, each non-inclusive, which is incorrect as there is a solid point at y = 3. However, the -4 non-inclusive part is correct.

Basically, this is all one function therefore there should be a single range. Since as you can see on the graph, 8 is included, the new range should be (-4, 8]. The function extends from -4, non-inclusive, to 8, inclusive. Even though there is a gap between the two parts, it is a singular function and as a whole, both are considered when calculating the range.

Question 2: C, {x | x > 10}

You are correct! x = 10 is a vertical asymptote for this function - the function will never reach this value so you should not use the "greater than or equal to" sign.

Ques 1)

The range of the function given in the graph in interval notion is:

                        (-4,8]

Ques 2)

The domain of the function given in the graph in set builder notation is:

                        {x| x≥10 }

Ques 1)

Range of a function--

The range of a function is the set of all the values which are attained by a function in it's defined domain.

By looking at the function we observe that the function takes all the values between -4 to 8.

Also the value -4 is excluded is from the range since there is a open circle at (-7,-4) and 8 is included in the range.

Since there is a closed circle at (2,8)

Hence, the range of the function is:

                      (-4,8]

Ques 2)

Domain of a function--

The domain of a function is the set of all the x-values for which the function is defined.

By looking at the function we observe that the function is defined for all x greater than or equal to 10.

Hence, the domain of the function is:

              {x| x≥10 }

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step-by-step explanation:

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