Chapter 1.4, Problem 88E

To determine

Find the matching and determining Constants.

Answer to Problem 88E

The function is $\boxed{h\left(x\right)=c\sqrt{\left|x\right|}}and\boxed{c=1}$

Explanation of Solution

Given information:

Match the data with one of the following functions and determine the value of the constant that will make the function fit the data in the table

  $f\left(x\right)=cx$ , $g\left(x\right)=c{x}^2$ , $h\left(x\right)=c\sqrt{\left|x\right|}$ and $r\left(x\right)=\frac{c}{x}$

  

Calculation:

Consider the given table.

  

  $f\left(x\right)=cx$ , $g\left(x\right)=c{x}^2$ , $h\left(x\right)=c\sqrt{\left|x\right|}$ and $r\left(x\right)=\frac{c}{x}$

From the above values, because the range has positive values for both negative and positive domain values so it is mandatory to have either $c{x}^2$ or $c\sqrt{\left|x\right|}$

The increasing values $y$ is less when compared with increasing values of $x$ .

This is possible only for $c\sqrt{\left|x\right|}$

It is proved that it is $h\left(x\right)$

Verifying the other points give the value of constant as $c=1$

Hence, the function is $\boxed{h\left(x\right)=c\sqrt{\left|x\right|}}and\boxed{c=1}$