Chapter 3.1, Problem 10CYU

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 10CYU

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

The range of the function is $y=-1$ .

Explanation of Solution

Given information:

Given equation,

  $-3+2y=-5$

Calculation:

Consider the given equation,

  $-3+2y=-5$

Solving for variable $y$

Adding 3 both sides

  $\begin{array}{c}-3+2y=-5\\ -3+3+2y=-5+3\\ 2y=-2\end{array}$

On dividing by 2 on both sides,

  $\begin{array}{c}\frac{2y}{2}=\frac{-2}{2}\\ y=-1\end{array}$

Here in this equation the variable $x$ is not given. Therefore, any value for $x$ can be chosen.

Making the table of values for the equation

$x$	$y$	$\left(x,y\right)$
0	$-1$	$\left(0,-1\right)$
1	$-1$	$\left(1,-1\right)$
2	$-1$	$\left(2,-1\right)$

Graph:

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

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

Here $y$ coordinate is always $-1$ . Therefore, the range of the function is $y=-1$ .