Chapter 4.1, Problem 48E

(a)

To determine

To describe: the degree and leading coefficient of $f$ .

Answer to Problem 48E

The degree of function is odd and leading coefficient is positive.

Explanation of Solution

Given information:

Given graph,

  

Calculation:

From the graph it is very clear that $f\left(x\right)\to -\infty$ as $x\to -\infty$ and $f\left(x\right)\leftarrow \infty$ as $x\to \infty$ .

Therefore, the degree of function is odd and leading coefficient is positive.

(b)

To determine

To describe: the intervals where the function is increasing and decreasing.

Answer to Problem 48E

Function is increasing for $x<-3\text{and}x>-1$ and decreasing for $-3<x<-1$ .

Explanation of Solution

Given information:

Given graph,

  

Calculation:

From the graph it is very clear that for all $-3<x<-1$ the $y$ values decreases as move from to right and for all $x<-3\text{and}x>-1$ the $y$ value increases as move from left to right.

Therefore, function is increasing for $x<-3\text{and}x>-1$ and decreasing for $-3<x<-1$ .

(c)

To determine

To find: the constant term of the polynomial function.

Answer to Problem 48E

The constant term is $a_0$ . $-3<x<-1$ .

Explanation of Solution

Given information:

Given graph,

  

Calculation:

To determine the constant term, evaluate $f\left(0\right)$ ,

  $\begin{array}{c}f\left(0\right)=a_n{\left(0\right)}^n+a_{n-1}{\left(0\right)}^{n-1}+\mathrm{...}+a_1\left(0\right)+a_0\\ =a_0\end{array}$

Therefore, the constant term is $a_0$ .