Answers:
Domain as an inequality: [tex]\boldsymbol{-\infty < \text{x} < \infty}[/tex]
Domain in interval notation: [tex]\boldsymbol{(-\infty , \infty)}[/tex]
Range as an inequality: [tex]\boldsymbol{-3 \le \text{y} \le 3}[/tex]
Range in interval notation: [-3, 3]
=================================================
Explanation:
The domain is the set of allowed x inputs. This graph goes on forever in both directions, so we can plug in any real number for x. There are no restrictions to worry about.
As an inequality, we write [tex]-\infty < \text{x} < \infty[/tex] to basically say "x is between negative infinity and infinity". In other words, x is anything on the real number line.
That inequality condenses into the interval notation of [tex](-\infty , \infty)[/tex]
Always use curved parenthesis for either infinity, because we can't ever reach infinity. It's not a number on the number line but rather a concept.
----------------------
Now onto the range.
Recall the range is the set of possible y outputs. We look at the lowest and highest points (aka min and max) to determine the boundaries for the range.
In this case, the smallest y can get is y = -3
The largest it can get is y = 3
The range is any value of y such that [tex]-3 \le \text{y} \le 3[/tex] which in word form is "any value between -3 and 3, inclusive of both endpoints".
That inequality condenses to the interval notation [-3, 3]
We use square brackets to include the endpoints as part of the range.
