Answer:
Domain: (-5, ∞)
Range: [-4, 1]
Explanation:
Domain is the set of all permissible values of x for the function. The smallest value of x is at x = -5. However note that there is an unfilled circle at x = -5 where y = -1. This means the point(-5, -1) is excluded in the function
The function flattens out at x = 3 and the arrow on the end of the function plot indicates that the x-value of the function goes up to ∞
The domain in interval form is (-5, ∞).
Be careful with the brackets. The regular parentheses ( and ) indicate that the extremes of the interval -5 and ∞ are not included in the interval. ∞ is never included. Such an interval is called an open interval.
The range is the set of y-values for the domain
Looking at the graph we can see that the lowest y value is -4 at x = -2 and it is a valid value for the function so included in the interval
The highest value of y is 1 and it becomes 1 at x =3 but since the plot after x = 2 is horizontal, that means the y value will be 1 for any value x >= 3
Therefore the range of the function is
[-4, 1]
Here note that we are using square brackets to indicate that -4 and 1 are included in the interval. Such an interval is called a closed interval.