Answer:
Explanation:
To graph the function f(x), we need to plot the points for the different intervals and connect them to create a continuous line. Let's break it down into two parts:
1. For the interval -9 ≤ x < 0:
The equation for this interval is f(x) = (-1/3)x - 4. We can select some values for x within this interval and calculate the corresponding values of f(x). Let's choose x = -9, -6, -3, -1.
For x = -9:
f(-9) = (-1/3)(-9) - 4 = 3 - 4 = -1
So, we have the point (-9, -1).
For x = -6:
f(-6) = (-1/3)(-6) - 4 = 2 - 4 = -2
So, we have the point (-6, -2).
For x = -3:
f(-3) = (-1/3)(-3) - 4 = 1 - 4 = -3
So, we have the point (-3, -3).
For x = -1:
f(-1) = (-1/3)(-1) - 4 = 1/3 - 4 = -3 2/3 ≈ -3.67
So, we have the point (-1, -3.67).
Plot these points on the graph.
2. For the interval 0 ≤ x ≤ 4:
The equation for this interval is f(x) = 2x. Similarly, we can select some values for x within this interval and calculate the corresponding values of f(x). Let's choose x = 0, 1, 2, 4.
For x = 0:
f(0) = 2(0) = 0
So, we have the point (0, 0).
For x = 1:
f(1) = 2(1) = 2
So, we have the point (1, 2).
For x = 2:
f(2) = 2(2) = 4
So, we have the point (2, 4).
For x = 4:
f(4) = 2(4) = 8
So, we have the point (4, 8).
Plot these points on the graph.
Now, connect the points for the respective intervals with a continuous line segment. The line segment for the interval -9 ≤ x < 0 will have a negative slope, and the line segment for the interval 0 ≤ x ≤ 4 will have a positive slope.
Your graph of f(x) will have a downward-sloping line from (-9, -1) to (-1, -3.67), and then it will have an upward-sloping line from (0, 0) to (4, 8).