What does the graph of y = absolute X-2 look like?
y = |x-2|
why not just take some simple values of x and see what points you get, then plot them
0,2
1,1
2,0
3,1
4,2
...
-1,3
-2,4
-3,5
..
can you see the pattern ?
Yes I can. Thank you from a 68 year old Grandfather helping his Grandson
To understand what the graph of y = absolute(x-2) looks like, let's break it down step by step.
The absolute value function, denoted by |x|, gives the distance of a number x from zero. It always returns a non-negative value.
In this case, we have y = absolute(x-2), which means that the y-value is the absolute value of the difference between x and 2.
To graph this equation, we can start by looking at the behavior of the function for different values of x:
1. When x is less than 2, (x-2) is negative, and the absolute value of a negative number is its positive counterpart. So, y = absolute(x-2) becomes y = -(x-2), which simplifies to y = -x + 2.
2. When x is greater than 2, (x-2) is positive, and the absolute value of a positive number remains the same. So, y = absolute(x-2) remains as y = x - 2.
By considering these two cases, we can plot points on the graph:
When x < 2:
- Let's choose x = 0. Substitute it into y = -x + 2:
y = -0 + 2 = 2, so we have the point (0, 2).
- Let's choose x = 1. Substitute it into y = -x + 2:
y = -1 + 2 = 1, so we have the point (1, 1).
When x > 2:
- Let's choose x = 3. Substitute it into y = x - 2:
y = 3 - 2 = 1, so we have the point (3, 1).
- Let's choose x = 4. Substitute it into y = x - 2:
y = 4 - 2 = 2, so we have the point (4, 2).
Now, we can plot these points on a graph and draw a line connecting them. The line will have a "V" shape, with the vertex at (2, 0). On the left side of the graph, the line slopes downward, and on the right side, it slopes upward.
So, the graph of y = absolute(x-2) is a "V" shape, centered at (2, 0), which opens upwards and downwards.