graph the following function on the set of axes below. f(x) = lxl, -3 less than or equal to x less than 1 and 4, 1 less than or equal to x less than or equal to 8

Ffc

To graph the function f(x) = |x| on the set of axes, we will first graph the two pieces of the function separately and then combine them.

1. Graphing the first piece: -3 ≤ x < 1
For this part of the function, we substitute x = -3, -2, -1, 0 into f(x) = |x| and plot the corresponding points on the graph.

When x = -3, f(-3) = |-3| = 3, so plot the point (-3, 3).
When x = -2, f(-2) = |-2| = 2, so plot the point (-2, 2).
When x = -1, f(-1) = |-1| = 1, so plot the point (-1, 1).
When x = 0, f(0) = |0| = 0, so plot the point (0, 0).
Connect these points with a line segment.

2. Graphing the second piece: 4, 1 ≤ x ≤ 8
For this part of the function, we substitute x = 4, 5, 6, 7, 8 into f(x) = |x| and plot the corresponding points on the graph.

When x = 4, f(4) = |4| = 4, so plot the point (4, 4).
When x = 5, f(5) = |5| = 5, so plot the point (5, 5).
When x = 6, f(6) = |6| = 6, so plot the point (6, 6).
When x = 7, f(7) = |7| = 7, so plot the point (7, 7).
When x = 8, f(8) = |8| = 8, so plot the point (8, 8).
Connect these points with a line segment.

3. Combine the graphs from step 1 and step 2.
Since the graph for -3 ≤ x < 1 is separate from the graph for 4, 1 ≤ x ≤ 8, draw a small gap between the two segments.

The final graph should look like a "V" shape, opening downwards, with one side connecting the points (-3, 3) and (0, 0), and the other side connecting the points (4, 4) and (8, 8).

To graph the function f(x) = |x|, we need to plot the points on the given intervals and connect them with lines.

First, let's focus on the interval -3 ≤ x < 1. In this interval, the function f(x) = |x| takes the absolute value of each x value. For any negative x values, the absolute value function will make them positive. For the positive x values, the function will keep them unchanged.

So, we can start by selecting some values within this interval and find their corresponding points on the graph.

Let's choose x = -3, -2, -1, and 0. For x = -3, we have f(-3) = |-3| = 3. For x = -2, we have f(-2) = |-2| = 2. For x = -1, we have f(-1) = |-1| = 1. Finally, for x = 0, we have f(0) = |0| = 0.

Plot these points on the graph.

Next, let's consider the interval 4 ≤ x ≤ 8. In this interval, the function f(x) = |x| behaves similarly. Any positive x value will remain the same, and any negative x value will be converted to its positive counterpart.

Let's choose x = 4, 5, 6, 7, and 8. For all these values, the absolute value function will keep them unchanged. So, f(4) = |4| = 4, f(5) = |5| = 5, f(6) = |6| = 6, f(7) = |7| = 7, and f(8) = |8| = 8.

Plot these points on the graph.

Lastly, we need to connect the points on the graph with lines. In this case, since the function is defined piece-wise, we will have two separate line segments. One for the interval -3 ≤ x < 1 and another for the interval 4 ≤ x ≤ 8.

After connecting the points, your graph should have two line segments. The first segment connects (-3, 3), (-2, 2), (-1, 1), and (0, 0). The second segment connects (4, 4), (5, 5), (6, 6), (7, 7), and (8, 8).

Make sure to label the x and y-axis accordingly and clearly indicate the break in the graph at x = 1.

I hope this explanation helps you graph the given function!

all those words!

f(x) =
|x| if -3 <= x < 1
4 if 1 <= x <= 8

Just plot each line, and mark off the sections you want.

http://www.wolframalpha.com/input/?i=plot+[piecewise+[{{|x|,+-3%3C%3Dx%3C1},{4,+1%3C%3Dx%3C8}}]]