Chapter 3.1, Problem 9CYU

To determine

To sketch: the graph of the given equation by making a table and to state the domain and the range.

Answer to Problem 9CYU

The domain of the given function is all real numbers $x\in R$ .

The range of the function is all real numbers $y\in R$ .

Explanation of Solution

Given information:

Given equation,

  $x+2y=4$

Calculation:

Consider the given equation,

  $x+2y=4$

Solving for variable $y$

  $\begin{array}{c}x+2y=4\\ 2y=4-x\end{array}$

On dividing by 2 on both sides,

  $y=\frac{\left(4-x\right)}{2}$

Making the table of values for the equation

$x$	$y$	$\left(x,y\right)$
0	$\frac{\left(4-0\right)}{2}=2$	$\left(0,2\right)$
2	$\frac{\left(4-2\right)}{2}=1$	$\left(2,1\right)$
4	$\frac{\left(4-4\right)}{2}=0$	$\left(4,0\right)$

Graph:

  

From the graph it is observed that the straight line extends from negative infinite to positive infinite along the $x$ and $y$ axis.

Therefore, the domain of the given function is all real numbers $x\in R$ .

The range of the function is all real numbers $y\in R$ .