Graph y=|x|-2.
If someone could help me that would be great.. Im really confused.
when x = 0, y = -2
Y increases at 45 degrees from there in both directions
so it is a V
with the bottom point at (0 , -2)
Just graph a few points working both ways from ( 0 , -2 )
To graph the equation y = |x| - 2, you can follow these steps:
Step 1: Set up a coordinate grid or graph paper to plot the points.
Step 2: Start by considering different values of x to find the corresponding y-values.
Step 3: When x is positive or equal to 0, the absolute value of x will be the same as x itself. So, if x is 0, then |x| will also be 0. Thus, when x is 0, y = 0 - 2 = -2.
Step 4: When x is negative, the absolute value of x will become positive. So, |x| will become -x. For example, if x is -3, then |x| will be |-3| = 3. Therefore, when x is negative, y = -x - 2.
Step 5: Now you can plot the points on the coordinate grid using the found x and y values. For x = 0, y = -2, so the point (0, -2) is plotted. For x = -3, y = -(-3) - 2 = 1 - 2 = -1. So, the point (-3, -1) is plotted.
Step 6: Connect the plotted points with a straight line. Since absolute value is always positive or zero, the graph will lie above the x-axis, and the line will have a "V" shape, opening upwards.
Step 7: Your graph is complete!
Here's a rough sketch of the graph:
|
|... |
..| ..|
.. | |
. | |
-2____|_____|
-3 0 3
Sure! I'd be happy to help you.
The equation you have, y = |x| - 2, represents a graph of a function. The function involves an absolute value, which means that the output (y-value) is the positive distance of the input (x-value) from zero, subtracted by 2.
To graph this equation, we can follow a few steps:
1. Firstly, let's identify some key points on the graph. We can start by finding the y-intercept, which is the value of y when x is 0.
- Substitute x = 0 into the equation: y = |0| - 2 = -2. So our y-intercept is (0, -2).
2. Next, we can find a few more points by selecting some x-values and calculating their corresponding y-values.
- Let's choose a few x-values, such as x = -2, -1, 1, and 2.
- Substitute those values into the equation and calculate the corresponding y-values:
For x = -2, y = |-2| - 2 = 2 - 2 = 0. So we have the point (-2, 0).
For x = -1, y = |-1| - 2 = 1 - 2 = -1. So we have the point (-1, -1).
For x = 1, y = |1| - 2 = 1 - 2 = -1. So we have the point (1, -1).
For x = 2, y = |2| - 2 = 2 - 2 = 0. So we have the point (2, 0).
3. Now that we have a few points, we can plot them on a coordinate grid and connect them to form the graph of the function y = |x| - 2.
- Plot the points we found: (0, -2), (-2, 0), (-1, -1), (1, -1), and (2, 0).
- Draw a straight line connecting these points.
The resulting graph should be a V-shape, with the tip of the V pointing downward, intercepting the y-axis at (0, -2).
I hope this helps! Let me know if you have any further questions.