Chapter 6.7, Problem 90SR

(a)

To determine

To Describe :

The end behaviour.

Answer to Problem 90SR

  $\begin{array}{l}\text{As x}\to \text{+}\infty \text{ , f(x)}\to +\infty \\ \text{and}\\ \text{As x}\to \text{ -}\infty \text{ , f(x)}\to -\infty \end{array}$

Explanation of Solution

Given Information:

Given graph is:

  

Calculation:

  $\begin{array}{l}\text{Clearly , from the graph we can observe that }\\ \text{As x}\to \text{+}\infty \text{ , f(x)}\to +\infty \\ \text{and}\\ \text{As x}\to \text{ -}\infty \text{ , f(x)}\to -\infty \\ Hence,\\ The\text{ function value tends to +}\infty \text{ as x value tends to +}\infty \\ \text{and}\\ \text{The function value tends to -}\infty \text{ as x value tends to -}\infty \end{array}$

(b)

To determine

Whether the graph represents odd-degree or even-degree polynomial function.

Answer to Problem 90SR

Odd degree polynomial function.

Explanation of Solution

Given Information:

Given graph is:

  

Calculation:

  $\begin{array}{l}From\text{ part (a), we have :}\\ \text{As x}\to \text{+}\infty \text{ , f(x)}\to +\infty \\ \text{and}\\ \text{As x}\to \text{ -}\infty \text{ , f(x)}\to -\infty \\ \text{Since the end behaviours are in the opposite directions, }\\ \text{the graph represents an odd-degree polynomial}\text{.}\end{array}$

(c)

To determine

The number of real zeroes

Answer to Problem 90SR

1

Explanation of Solution

Given Information:

Given graph is:

  

Calculation:

  $\begin{array}{l}\text{Zeroes of a function is the value where the function value is 0, }\\ \text{or where the graph of the function intersects the x-axis}\text{.}\\ \text{The given graph intersects the x-axis at 1 point , so the number }\\ \text{of real zeroes is 1}\text{.}\end{array}$

Hence the simplified form of the expression is $-i$ .