Chapter 3.9, Problem 2OE

To determine

To Find: The missing entries in the table.

Answer to Problem 2OE

The answer is $-1\text{and}-3.$

Explanation of Solution

Given information:Given values is a linear function.

Calculation:

Let the given linear function is $f(x)=ax+b$

From the table, we get

  $\begin{array}{l}\text{when}x=0\text{we}\text{get}f(x)=3\text{put}\text{these}\text{values}\text{on}\text{the}\text{above}\text{function}\\ 3=a\times 0+b\\ b=3\mathrm{...}(1)\\ \text{Similarly,}\\ \text{when}x=1\text{we}\text{get}f(x)=1,\text{than}\\ 1=a\times 1+b\\ a+b=1\mathrm{...}(2)\\ a+3=1\text{from}(1)\\ a=1-3\\ a=-2\end{array}$

So, the required function is $f(x)=-2x+3$

Now,

  $\begin{array}{l}\text{when}x=2\\ f(x)=-2\times 2+3\\ f(x)=-4+3\\ f(x)=-1\\ \text{and}\text{when}x=3\\ f(x)=-2\times 3+3\\ f(x)=-6+3\\ f(x)=-3\end{array}$

Thus, the missing values are $-1\text{and}-3.$