Chapter 11.5, Problem 43PPS

(a)

To determine

To calculate: To rewrite the function as a quotient plus a remainder and the graph the quotient

Answer to Problem 43PPS

Function as a quotient plus a remainder is $f\left(x\right)=3+\frac{7}{x-1}$

Explanation of Solution

Given information: $f\left(x\right)=\frac{3x+4}{x-1}$

Formula Used:

Long division is the division of whole number in a systematic procedure to derive the answer.

Calculation:

Function is given as follows:

  $f\left(x\right)=\frac{3x+4}{x-1}$

Dividing the expression with the divisor to derive the quotient and remainder:

  $x-1\begin{array}{c}\hfill 3\\ \hfill \overline{)\begin{array}{l}3x+4\\ 3x-3\\ -+\\ ----\\ 7\end{array}}\end{array}$

Thus, function as a quotient plus a remainder is

  $f\left(x\right)=3+\frac{7}{x-1}$

Here, quotient is $3$

Graph of $f\left(x\right)=3$ is plotted as follows:

  

Conclusion:

Hence, function as a quotient plus a remainder is $f\left(x\right)=3+\frac{7}{x-1}$

(b)

To determine

To calculate: To graph the function

Explanation of Solution

Given information: $f\left(x\right)=\frac{3x+4}{x-1}$

Calculation:

Function is given as follows:

  $f\left(x\right)=\frac{3x+4}{x-1}$

When $x=0$

  $f\left(x\right)=\frac{3\left(0\right)+4}{0-1}=\frac{4}{-1}=-4$

When $x=2$

  $f\left(2\right)=\frac{3\left(2\right)+4}{2-1}=\frac{6+4}{1}=10$

Graph of $f\left(x\right)=\frac{3x+4}{x-1}$ is plotted as follows:

  

Conclusion:

Hence, graph of function is plotted