Question

What are the terminal points, asymptotes, and highest and lowest vertex of the function y = √(x-4) + 4?

A) Terminal points: (4, 4)
B) Terminal points: None
C) Asymptotes: x = 4
D) Asymptotes: y = 4

Answer 1

The terminal points of the function y = √(x-4) + 4 are (4, 4). There are no asymptotes for this function. The highest and lowest vertex of the function are both (4, 4).

Step-by-step explanation:

The given function is y = √(x-4) + 4.

To find the terminal points, we need to determine the values of x that make the square root term equal to zero. So, we set (x-4) = 0 and solve for x. This gives us x = 4. So, the terminal point is (4, 4).

There are no asymptotes for this function because there are no restrictions on the values of x or y.

The highest vertex occurs at the point where the square root term is equal to its maximum value, which is 0. Therefore, the highest vertex is (4, 4). The lowest vertex occurs at the point where the square root term is equal to its minimum value, which is 0. Therefore, the lowest vertex is also (4, 4).