Chapter 4.1, Problem 24E

To determine

To writelinear function $f$ with the given values −

  $f\left(0\right)=3$ and $f\left(-6\right)=3$

Answer to Problem 24E

The linear function is $f\left(x\right)=3$ .

Explanation of Solution

Given:

  $f\left(0\right)=3$

  $f\left(-6\right)=3$

Formula Used:

The equation of a line is written as $f\left(x\right)=mx+b$ where m is the slope and $b$ is the $y$ -intercept.

  $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Given:

  $f\left(0\right)=3$

  $f\left(-6\right)=3$

As per the above definition, we have equation of the line as

  $f\left(x\right)=mx+b$

Since, $f\left(0\right)=3$ , thus we have:

  $\begin{array}{l}3=\left(m\times 0\right)+b\\ b=3\end{array}$

Since, $f\left(-6\right)=3$ and $b=3$ , thus we have:

  $\begin{array}{l}3=\left(m\times -6\right)+3\\ 0=m\\ m=0\end{array}$

Thus, the equation of the line −

  $\begin{array}{l}f\left(x\right)=\left(0\times x\right)+3\\ f\left(x\right)=3\end{array}$

Thus, the linear function is $f\left(x\right)=3$ .

Conclusion:

Hence, the linear function is $f\left(x\right)=3$ .