Question

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Answer 1

The graph shows the height of a kicked soccer ball f(x), in feet, depending on the distance from the kicker x, in feet

Part A: What do the x-intercepts of the graph represent?

The x intercept means value of x when h(x)=0. That is, the x-intercept signify the distance from kicker when height h(x) =0. The x intercept is (0,0) and (16,0).

So, when the kicker is at a distance of 0 feet or 16 feet, height h(x)=0 feet.

What does maximum value of the graph represent?

The maximum value of the graph signify maximum height the soccer ball can achieve. The maximum height the graph has is at (8,10). That is, when kicker is at a distance of 8 feet from the ball, the ball attains a maximum height of 10 feet.

What are the intervals where the function is increasing and decreasing, and what do they represent about distance and height?

The increasing interval is (-∞,8]. That is, the height of the ball increases when kicker is increasing as the distance increases from -∞ to 8. But, the height keeps on decreasing from 8 to ∞. As, x, distance increases from 8, the height decreases, Hence, decreasing interval [8,∞)

Part B: What is an approximate average rate of change of the graph from x=8 to x=13, and what does this rate represent?

average rate of change=$\frac{f(x2)-f(x1)}{x2-x1}$

where x2=13 and x1=8. That is, the interval in which we are looking for average rate of change

f(x2)=f(13)=5

f(x1)=f(8)=10

average rate of change =$\frac{5-10}{13-8}$

=$\frac{-5}{5}$

=-1

average rate of change =-1.

This rate signify that height decreases by 1 feet as distance of the skipper increases by 1 feet (when distance, x is between 8 and 13)