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 _____

Answer 1

A) 1.yes

B) The domain is All real numbers.

Step-by-step explanation:

The problem gives us a relationship:

`y=(x+2)/(5)`

For this relationship to be a function, for each value of x, we should get a single value of y. We can see that this is true, given a value of x, we get a unique value of y. Thus, A is true.

Now, we need to find the domain. The domain is the set of all values of x for which the function is defined. In this case, the function is a line:

`\begin{gathered} y=(x+2)/(5) \\ . \\ y=(x)/(5)+(2)/(5) \\ . \\ y=(1)/(5)x+(2)/(5) \end{gathered}`

The equation is a line with slope 1/5 and y-intercept 2/5. We know that any line is defined for all real numbers.

Thus, the domain is all real numbers.