Chapter 3.9, Problem 13WE

To determine

To find: An equation of the linear function $f$ .

Answer to Problem 13WE

Therefore, the equation of linear function $f\left(x\right)=2x+1$ .

Explanation of Solution

Given information: The function $f\text{ at }x=0$ and $f\text{ at }x=3$ ,

  $f\left(0\right)=1,f\left(3\right)=7$

Formula used: For calculation of equation of linear function,

  $\begin{array}{l}f\left(x\right)=mx+b\\ \text{where }m\text{ is slope and b is }y-\text{intercept}\text{.}\end{array}$

Calculation: To calculate the equation of function using function $f\text{ at }x=0\text{ and }f\text{at }x=3$ ,

  $\begin{array}{l}\text{Putting value of }f\left(0\right)\text{in genral form,}\\ f\left(x\right)=mx+b\\ \text{Now, at }x=0\\ f\left(0\right)=m\times 0+b\\ b=1\\ \text{Putting value of }f\left(3\right)\text{in genral form,}\\ f\left(x\right)=mx+b\\ \text{Now, at }x=3\\ f\left(3\right)=m\times 3+1\\ 7=3m+1\\ m=2\\ f\left(x\right)=2x+1\end{array}$

Therefore, the equation of linear function $f\left(x\right)=2x+1$ .