Answer:
Step-by-step explanation:
Range of the function is the set of y-values (output values) of the function on the graph.
Domain of the function is the set of x-values (input values) of the function.
Domain of the function : [-5, 4)
(including x = -5 and excluding x = 4)
Range : [-4, 2)
(Including y = -4 and excluding y = 2)
x - intercepts : x = -5, -2, 2
Average rate of change over the interval [0, 2]
= [tex]\frac{f(2)-f(0)}{2-0}[/tex]
= [tex]\frac{0-(-4)}{2-0}[/tex] [Since, f(2) = 0, f(0) = -4]
= 2
Right most interval where the graph is positive → [2, 4]
The key feature of a function include the intercepts and intervals of the function
(a) The range
The least y value on the graph is at y = -4, and the maximum is at y = 2, with an open circle.
So, the range is:
[tex]\mathbf{Range = [-4,2)}[/tex]
(b) The domain
The least x value on the graph is at x = -5, and the maximum is at x = 4, with an open circle.
So, the domain is:
[tex]\mathbf{Domain = [-5,4)}[/tex]
(c) The x-intercepts
This is the point where the graph crosses the x-axis.
So, we have:
[tex]\mathbf{x-intercept =-2 \ and\ 2}[/tex]
(d) Average rate of change over [0,2]
From the graph, we have:
f(0) = -4
f(2) = 0
So, the average rate of change (m) is:
[tex]\mathbf{m = \frac{f(2) - f(0)}{2 - 0}}[/tex]
[tex]\mathbf{m = \frac{0 - -4}{2 - 0}}[/tex]
[tex]\mathbf{m = \frac{4}{2}}[/tex]
[tex]\mathbf{m =2}[/tex]
(d) The right-most interval where the graph is positive
The graph is positive from x = 2 to x = 4.
Hence, the right-most interval where the graph is positive is [2,4]
Read more about features of a function at:
https://brainly.com/question/17343786
