Chapter 8.4, Problem 56E

(a)

To determine

To find: The domain and range of the function

Answer to Problem 56E

The domain of the function would be $15\le x\le 45$

The range of the function would be $0\le f\left(x\right)\le 25$

Explanation of Solution

Given information:

The function is given as $f\left(x\right)=-\frac{1}{9}{\left(x-30\right)}^2+25$

Calculation:

  

The domain of the function would be $15\le x\le 45$

The range of the function would be $0\le f\left(x\right)\le 25$

Conclusion:

The domain of the function would be $15\le x\le 45$

The range of the function would be $0\le f\left(x\right)\le 25$

(b)

To determine

To find: the domain and range of the function $g\left(x\right)=f\left(x+5\right)$

Answer to Problem 56E

The domain of the function would be $10\le x\le 40$

The range of the function would be

  $0\le f\left(x\right)\le 25$

Explanation of Solution

Given information:

The height is given as $g\left(x\right)=f\left(x+5\right)$

Calculation:

  

The domain of the function would be $10\le x\le 40$

The range of the function would be $0\le f\left(x\right)\le 25$

Conclusion:

The domain of the function would be $10\le x\le 40$

The range of the function would be $0\le f\left(x\right)\le 25$

(c)

To determine

To find: the point at which the kicker punt closer to his goal line.

Answer to Problem 56E

The kicker kicks closer to the goal line in the second try

Explanation of Solution

Given information:

  $g\left(x\right)=f\left(x+5\right)$

  $f\left(x\right)=-\frac{1}{9}{\left(x-30\right)}^2+25$

Calculation:

The graph of $f\left(x\right)$ is a translational right of 5 units to the graph of $g\left(x\right)$ . The kicker kicks closer to the goal line in the second try

Conclusion:

The kicker kicks closer to the goal line in the second try