5. the graph below shows a curve. on what interval(s) is the curve decreasing? answer:
5. the graph below shows a curve. on what interval(s) is the curve decreasing? answer:
Answer
Explanation:
Step1: Understand the concept of a decreasing function
A function (y = f(x)) is decreasing on an interval if for any two points (x_1) and (x_2) in the interval with (x_1<x_2), we have (f(x_1)>f(x_2)). Visually, on a graph, the function has a negative slope.
Step2: Analyze the given graph
Looking at the graph, we can observe the behavior of the curve. The (x -)axis is the independent - variable axis. We check the intervals between the key - points (the points where the direction of the curve changes). Let's assume the key - points on the (x -)axis (the horizontal axis) are at (x = 4) and (x = 6). For the interval ([4,6]), as (x) increases from (4) to (6), the (y) - value (the value of the function) decreases.
Answer:
The curve is decreasing on the interval ([4,6])