Question

Can someone please help me with this math problem? The math problem is listed in the picture, Thanks!

I can only use numbers, infinity symbols, etc.


You have to consider the following relation.

Answer 1

Answer:

Domain:

$- \infty < x < \infty$

Range:

$- 1 \le \: y < \infty$

Step-by-step explanation:

Domain:

The Domain of a function is x values which are included in the graph. Sometimes x values will not be included because they cannot be defined at that point, but in this case the graph indicates that the graph continues to the right and left with no indication that there is an asymptote or it is undefined beyond the graph so we can assume it's defined for all real numbers. We can represent this in interval notation as:

$- \infty < x < \infty$

Since if you plug in any real number, this inequality should be true.

Range:

The range of a function is defined as y values which are on the graph, this is restricted when certain y values are not on the graph... but we can usually tell because functions will have a minimum/maximum. By looking at the graph it appears to reach a minimum at y = -1 and then on the right and left side is increasing, never going below this value, so the range can be defined as:

$- 1 \le y < \infty$

Since the y values vary between -1 (including -1) and infinity... well that really just means there's no upper bound and it just keeps increasing and increasing.