Chapter 6.4, Problem 38PPS

(a)

To determine

To find: The value of relative maxima and minima.

Answer to Problem 38PPS

The value of relative maxima are $x=-3\cdot 5$ , $x=-1\cdot 75$ and $x=1$ , and relative minima are $x=-2\cdot 5$ , $x=-1$ and $x=2$ .

Explanation of Solution

Given information:

The givengraph is shown in figure (1).

  

Figure (1)

Calculation:

From the given graph.

The values of relative maxima are at $x=-3\cdot 5$ , $x=-1\cdot 75$ and $x=1$ .

The values of relative minima are at $x=-2\cdot 5$ , $x=-1$ and $x=2$ .

Therefore,the value of relative maxima are $x=-3\cdot 5$ , $x=-1\cdot 75$ and $x=1$ , and relative minima are $x=-2\cdot 5$ , $x=-1$ and $x=2$ .

(b)

To determine

To find: The value of $x-$ coordinate of every zero.

Answer to Problem 38PPS

The zeroes are at $x=-4,-3,0,1\cdot 5,\text{and}2\cdot 7\text{5}$ .

Explanation of Solution

Given information:

The given graph is shown in figure (1).

  

Figure (1)

Calculation:

From the given graph.

The zeroes are at $x=-4,-3,0,1\cdot 5,\text{and}2\cdot 7\text{5}$ .

Therefore, the zeroes are at $x=-4,-3,0,1\cdot 5,\text{and}2\cdot 7\text{5}$ .

(c)

To determine

To find: The smallest possible degree of the function.

Answer to Problem 38PPS

The smallest possible degree of the function is $7$ .

Explanation of Solution

Given information:

The given graph is shown in figure (1).

  

Figure (1)

Calculation:

From the given graph it is observed that the graph has $6$ turning points, the smallest possible degree of the polynomial function is $\left(6+1\right)$ or $7$ .

Therefore, the smallest possible degree of the function is $7$ .

(d)

To determine

To find: The domain and range of the function.

Answer to Problem 38PPS

The domain of the function is $\left\{\text{all}\text{real}\text{nunbers}\right\}$ and range is $\left\{\text{all}\text{real}\text{nunbers}\right\}$ .

Explanation of Solution

Given information:

The given graph is shown in figure (1).

  

Figure (1)

Calculation:

From the given graph.

The domain is: $\left\{\text{all}\text{real}\text{nunbers}\right\}$ .

The range is: $\left\{\text{all}\text{real}\text{nunbers}\right\}$

Therefore, the domain of the function is $\left\{\text{all}\text{real}\text{nunbers}\right\}$ and range is $\left\{\text{all}\text{real}\text{nunbers}\right\}$ .