Question

Decide whether the relation defines y as a function of x. Give the domain. x+2y = ——— 5A) Does the equation describe y as a function of x?1. Yes2. NoB) Give the domainThe domain is _____(Write the answer in interval notion. Use integers or fractions for any numbers in the expression.)

Answer 1

Given:

$y=\frac{x+2}{5}$

Required:

We need to find the domain of the given function if it is a function.

Explanation:

We need to graph the given equation.

Set x =3 and substitute in the given equation.

$y=\frac{3+2}{5}=\frac{5}{5}=1$

We get the point (3,1).

Set x =8 and substitute in the given equation.

$y=\frac{8+2}{5}=\frac{10}{5}=2$

We get the point (8,2).

Mark the points (3,1) and (8,2) in the graph and join them by ray.

it is not possible to draw a vertical line to touch the graph of a function in more than one place. Since it is a line.

Recall that If it is not possible to draw a vertical line to touch the graph of a function in more than one place, then y is a function of x.

The given relation is a function.

The answer for A) is Yes.

Recall that the domain of a graph consists of all the input values shown on the x-axis.

The line has no end on both sides,

For all real values, the function is valid.

The answer for B is

$Domain=(-\infty,\infty)$