Question

with aging, body fat increases and muscle mass declines. the graph to the right shows the percent body fat in a group of adult women and men as they age from 25 to 75 years. age is represented along the x - axis, and percent body fat is represented along the y - axis. state the intervals on which the graph giving the percent body fat in men is increasing and decreasing. on what interval is the graph increasing? a. (25,75) b. (20,26) c. (25,45) d. (45,75) on what interval is the graph decreasing? a. (45,75) b. (25,75) c. (25,45) d. (20,40)

Explanation:

Step1: Understand the concept of increasing and decreasing intervals

A function (or a graph) is increasing on an interval if, as \(x\) - values increase (move from left to right on the \(x\) - axis), the \(y\) - values also increase. A function is decreasing on an interval if, as \(x\) - values increase, the \(y\) - values decrease.

Step2: Analyze the graph for men (blue line)

• For the increasing part:

We look at the men's graph (blue line). As we move from \(x = 25\) to \(x=45\) (left - to - right on the \(x\) - axis), the \(y\) - values (percent body fat) are going up.

• For the decreasing part:

As we move from \(x = 45\) to \(x = 75\) (left - to - right on the \(x\) - axis), the \(y\) - values (percent body fat) are going down.

Answer:

• On what interval is the graph increasing? C. \((25,45)\)
• On what interval is the graph decreasing? A. \((45,75)\)