Question

I need help ASAP please someone help!

Answer 1

Answer: Choice A.  $(-\infty, \infty)$

This is the same as saying the set of all real numbers.

There are no restrictions to put on the domain, so there are no values to avoid. This is because there are gaps, jumps, or holes in the graph. It's one continuous single curve.

This curve stretches forever to the left and right. As it goes left, it moves up (rises to the left). As it moves right, it goes downhill (it falls to the right). Saying "rises to the left and falls to the right" is an informal way to describe the end behavior. The actual specific end behavior doesn't matter. What matters is both left and right sides go on forever.

A domain of the set of all real numbers means we can plug in any real number for x, and get some output for y, which is part of the range.

One way we can describe the set of all real numbers in terms of an inequality is to write $-\infty < x < \infty$ meaning that x is between negative and positive infinity, ie x is anything you want. The inequality $-\infty < x < \infty$ converts to the interval notation $(-\infty, \infty)$. Interval notation is a compact way of writing compound inequalities.