Question

Pre calculus help please!!! 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?

Answer 1

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 > 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.

Answer 2

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≥10

Explanation:

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