3. Graph the step function over the interval -2 ≤ x ≤ 2.
f(x) = |x+3|
So far I've got a plot over (-2,0) and (0,3) but I have no clue if I'm doing it right! May I get some help?
For x = - 2
| x + 3 | = | - 2 + 3 | = | 1 | = 1
For x = 2
| x + 3 | = | 2 + 3 | = | 5 | = 5
In Cartesian coordinate system mark points ( - 2 , 1 ) and ( 2 , 5 )
and draw line
|x+3| is not a step function
⌊x+3⌋ is a step function
plot (-2,1) with a solid dot. Draw a horizontal line to (-1,1)
plot (-1,2) with a solid dot. Draw a horizontal line of length 1
and so on. it looks like a staircase -- with steps
Sure, I'd be happy to help you with graphing the step function!
The step function |x+3| represents the absolute value of the expression x+3. To graph it, we can break it down into two separate cases based on the sign of x+3.
Case 1: When x+3 is positive or zero (x+3 ≥ 0):
In this case, the absolute value function simplifies to |x+3| = x+3. So we can plot the function as a line passing through the points (-2, 1), (-1, 0), (0, 3), and (2, 5).
Case 2: When x+3 is negative (x+3 < 0):
In this case, the absolute value function simplifies to |x+3| = -(x+3). So we can plot the function as a line passing through the points (-3, 0), (-2, -1), and (-1, -2).
Here is the graph of the step function f(x) = |x+3| over the interval -2 ≤ x ≤ 2:
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Keep in mind that the points I provided are just estimates, and you may want to use graphing software or a ruler to get more precise points.
I hope this helps! Let me know if you have any more questions or need further assistance.
Sure! I'd be happy to help you with graphing the step function f(x) = |x+3| over the interval -2 ≤ x ≤ 2.
To graph a step function, we need to understand how it behaves in different intervals. In this case, we have two intervals to consider: x ≤ -3 and x > -3.
First, let's consider the interval x ≤ -3:
For x ≤ -3, the expression inside the absolute value |x+3| becomes negative. Therefore, when we substitute x ≤ -3 into f(x) = |x+3|, we get f(x) = -(x+3), because the negative sign within the absolute value function will change the sign of the expression.
Next, let's consider the interval x > -3:
For x > -3, the expression inside the absolute value |x+3| becomes positive. Therefore, when we substitute x > -3 into f(x) = |x+3|, we get f(x) = x+3, because the positive sign within the absolute value function will keep the sign unchanged.
Now, let's focus on plotting the graph:
1. For x ≤ -3:
a) Choose some x-values that are less than or equal to -3. For example, you can choose x = -4, -5, -6, etc.
b) Substitute these x-values into f(x) = -(x+3) to find the corresponding y-values.
c) Plot the points (-4, f(-4)), (-5, f(-5)), (-6, f(-6)), and so on.
2. For x > -3:
a) Choose some x-values that are greater than -3. For example, you can choose x = -2, -1, 0, 1, 2, etc.
b) Substitute these x-values into f(x) = x+3 to find the corresponding y-values.
c) Plot the points (-2, f(-2)), (-1, f(-1)), (0, f(0)), (1, f(1)), (2, f(2)), and so on.
Remember that the step function jumps from one expression to another at the boundary point, which is x = -3 in this case. So you will have two separate sets of points.
Once you have all the points, connect them with straight lines to get the graph of the step function.
Hope this helps! Let me know if you have any further questions.