Answer:
Domain: [tex]-4<x\leq 4[/tex]
Range: [tex]-1\leq x\leq 3[/tex]
x-intercepts: x= -3, -1, 4
y-intercepts: y=1
Interval increasing: [-2,2]
Interval decreasing: (-4,-2] ∪ [2,4]
Rate of change over [2,4]: -1.5
Step-by-step explanation:
The domain of the function is the area it covers on the x-axis. This function goes from -4 to 4 so the domain would be [tex]-4<x\leq 4[/tex]
The less than symbol is used between -4 and x because the hole is open at x=-4. The less than or equal to symbol is used between x and 4 because the hole is solid at x=4.
The range of a function is the area it covers on the y-axis. This function goes from x=-1 to x=3 so the range would be [tex]-1\leq x\leq 3[/tex]
The x-intercepts for this function are everywhere the function crosses the x-axis. These are at x= -3, x= -1, and at x=4.
The y-intercepts for this function are everywhere the function crosses the y-axis. The only y-intercept is at y=1.
The intervals that are increasing are the segments on the graph that have a positive slope. The only increasing interval on this graph is from (-2,-1) to (2,3). This can be written as [-2,2] in interval notation.
The intervals that are decreasing are the segments on the graph that have a negative slope. These are from (-4,1) to (-2,-1) and from (2,3) to (4,0). This can be written as (-4,-2] ∪ [2,4]. Note that a parenthesis was used instead of a bracket in part of this expression. This is because of the open hole at x= -4.
The rate of change over an interval is the slope of that interval. Assuming [2,4] is referring to the x-coordinates on the interval, the rate of change can be calculated:
[tex]rate=\frac{3-0}{2-4}=\frac{3}{-2}=-1.5[/tex]
