Answer:
[tex]\textsf {Domain} : -\infty \: < x < \infty \\\textsf {In interval notation: } (-\infty, \infty)}[/tex]
[tex]\textsf {Range: } f\left(x\right)\le \:2 \\\textsf {In interval notation:} \:(-\infty \:,\:2][/tex]
Step-by-step explanation:
There are no undefined points for the function. So the domain is the set of all x values
The domain of x is (-∞, ∞) so x can be negative or positive. However, |x| is always positive
So if the inequality |x| + y ≥ 2 is to hold good then y has to be less than equal to 2, otherwise the left side drops below 2 and the inequality is not satisfied.
So the range is the set of all values in the interval (-∞, 2)
Check out the graph for a visual interpretation
