Chapter 4.4, Problem 27E

To determine

To evaluate the below function when $x=-3,0$ and $4$ -

  $f\left(x\right)=5x-8$

Answer to Problem 27E

  $x$ and $f\left(x\right)$ represents a positive correlation.

Explanation of Solution

Given:

  $f\left(x\right)=5x-8$

  $x=-3,0$ and $4$ -

Formula Used:

Correlation is positive when both the values increases or decreases together .

Calculation:

Given:

  $f\left(x\right)=5x-8$

  $x=-3,0$ and $4$ - Now, putting the values of $x$ in the above equation, we have:

When $x=-3$

  $\begin{array}{l}f\left(x\right)=5x-8\\ f\left(x\right)=\left(5\times -3\right)-8\\ f\left(x\right)=-23\end{array}$

When $x=0$

  $\begin{array}{l}f\left(x\right)=5x-8\\ f\left(x\right)=\left(5\times 0\right)-8\\ f\left(x\right)=-8\end{array}$

When $x=4$

  $\begin{array}{l}f\left(x\right)=5x-8\\ f\left(x\right)=\left(5\times 4\right)-8\\ f\left(x\right)=12\end{array}$

Thus, the table is −

$x$	$-3$	$0$	$4$
$f\left(x\right)$	$-23$	$-8$	$12$

Plotting the above points on a graph, we have:

  

The above points represent a straight line and a positive correlation between $x$ and $f\left(x\right)$ .

Conclusion:

  $x$ and $f\left(x\right)$ represents a positive correlation.