Question

Finding the domain and range of a function without a graph?

I know the answer, I just don't know how to get there.

Answer 1

Answer:
Domain:
`{ x \in R }`
Range:
`y \in R`

Explanation: Domain and range are all about restrictions within the x and y-ordinates.

Let's first talk about domain:
Essentially, the big question is "what can't x be?"
If x can be any number, then the domain will be under the set:
`{ x \in R }`
If x can't be a specific number, then the domain will still be under
`{ x \in R; x \\eq value }`

So, since we have a straight line, x can be any number, hence:
`{ x \in R }`

Range:
The range is a little bit harder for more complex graphs, such as the graph of
`e^(x) \cdot sinx`, but if it's a straight line, then we know that y can be any value. Any input will produce an output, and an output can produce an input.

Hence, the range will become:
`{ y \in R }`

Answer 2

The domain is the set of all possible x-values which will make the function "work" and will output real y-values.
The range is the resulting y-values we get after substituting all the possible x-values.

Since there is no square root or fraction involved with this equation, it can be assumed that the Domain is all real numbers as well as the Range is all real numbers.