Question

Complete the inequality below to describe the

domain of the graph shown.
Domain:
DONE
Complete the inequality below to describe the
range of the graph shown.
Range:
≤y <5
DONE
Intro
-5
5
y
5
X

Answer 1

`Domain: \;\boxed{-4 } < x \le 4\\\\Ramge: \boxed{-2} \le y < 5`

Explanation:

Domain

Domain is the set of all valid x values for the function
Looking at the graph we see that the function x values go from x- 4 to x = +4.

Note the unfilled circle at x = -4, y = 5. This means that this point is not included in any set of values that we intend tp find. It will represent a < or > inequality.

A filled circle means that value is included

So the domain of the function is -4 < x ≤ 4 (note that -4 is not included in the domain

Range
The range is the set of all y values for the entire domain. Basically it is defined using the min and max values that y can take

The minimum y value occurs at x = 4 and y is -2 (this is included because of the filled circle)

The max value occurs at x = -4 and the value of y here is 5 (5 is not included)

Therefore the range is -2 ≤ y < 5