Chapter 4, Problem 7CT

(a)

To determine

To find: The number of zeros of the given expression.

Answer to Problem 7CT

The required number of zeros of the functions is $4$ .

Explanation of Solution

Given information:

The given equation is:

  $\begin{array}{l}g\left(x\right)={\left(x-3\right)}^4\\ f\left(x\right)=x^4\end{array}$

Consider the graph of the functions:

  

Consider the given expression:

  $\begin{array}{l}g\left(x\right)={\left(x-3\right)}^4\\ f\left(x\right)=x^4\end{array}$

Is it seen that the degree of the functions are $4$

Hence, the number of zeros of the functions is $4$ .

(b)

To determine

To find: The relation between the two functions.

Answer to Problem 7CT

The graph shifts to the right by $3$ units.

Explanation of Solution

Given information:

The given equation is:

  $\begin{array}{l}g\left(x\right)={\left(x-3\right)}^4\\ f\left(x\right)=x^4\end{array}$

Consider the graph of the functions:

  

Consider the given expression:

  $\begin{array}{l}g\left(x\right)={\left(x-3\right)}^4\\ f\left(x\right)=x^4\end{array}$

Is it seen that the graph shift by $3$ units at the right side.

Hence, the graph shifts to the right by $3$ units.

(c)

To determine

To find: The increase and decrease of a function using the graph.

Explanation of Solution

Given information:

The given equation is:

  $\begin{array}{l}g\left(x\right)={\left(x-3\right)}^4\\ f\left(x\right)=x^4\end{array}$

Consider the graph of the functions:

  

Is it seen that the graph increases if goes upward by $3$ units and decreases if goes downward by $3$ units.