Question

Consider the function graphed. The function has a minimum value of ____ at x = ____.

A. 1, 2
B. 2, 1
C. 3, 5
D. -2, 3

The function is increasing on the open interval(s):
A. (1, 2)
B. (2, 3)
C. (3, 4)
D. (4, 5)

The function is decreasing on the open interval(s):
A. (1, 2)
B. (2, 3)
C. (3, 4)
D. (4, 5)

Answer 1

The function has a minimum value of 1 at x = 2 (Option A).

The function is increasing on the open interval(s) (2, 3) (Option B).

The function is decreasing on the open interval(s) (3, 4) (Option C).

Step-by-step explanation:

In the given options, the correct answer for the minimum value of the function is 1 at x = 2 (Option A). To determine this, we look for the lowest point on the graph, which corresponds to the minimum value of the function. In this case, it occurs at x = 2.

Now, let's analyze the intervals where the function is increasing and decreasing. The function is increasing on the open interval (2, 3) (Option B). This means that as x varies between 2 and 3, the function values are increasing.

Conversely, the function is decreasing on the open interval (3, 4)(Option C). During this interval, as x varies between 3 and 4, the function values are decreasing.

To visually identify these characteristics on a graph, we observe the slopes of the graphed function. An increasing function has a positive slope, and a decreasing function has a negative slope. By examining the given intervals, we can determine the corresponding changes in the function's behavior.