Need help with math question. Graph y=|x-2|?

Question

I really just need a reminder of what the lines mean. I seem to recall that it has something to do with absolute value? If anyone can fill in the blanks, I would really appreciate it. Thanks

Answer 1

Let's start with graphing y=|x|, or in English, y is equal to the absolute value of x.

When x is positive, y=x.
When x is negative, y = the positive value of x.

So, the graph of y=|x| looks like a V. The bottom of the V is at (0,0). The arms of the V head up with a slope of 1. Where x=-1, y=1. Where x=-2, y=2. Where x=+1, y=1. Where x=+2, y=2. And so on.

If that's the graph of y=|x|, what does the graph of y=|x-2| look like? Well, the -2 part just shifts the graph to the right 2. So, it's still a V, but now the bottom of the V is at (2,0). The arms of the V have the same slope of 1. At x=1, y=1. At x=0, y=2. At x=3, y=1. At x=4, y=2. And so on.

Answer 2

Yes, it is the absolute value of (x-2). That means that if (x-2) is negative, make it positive, and if it is positive, leave it positive. If it is zero, leave it zero.
Here are some answers:
x y
-10 12
-9 11
-8 10
-7 9
-6 8
-5 7
-4 6
-3 5
-2 4
-1 3
0 2
1 -1
2 0
3 1
4 2
5 3
6 4
7 5
8 6
9 7
10 8

Answer 3

The vertical lines *do* represent absolute value.

If you plug in values of x, you should get a table of y as follows:

x, y
-5, 7
-4, 6
-3, 5
-2, 4
-1, 3
0, 2
1, 1
2, 0
3, 1
4, 2
5, 3
6, 4
7, 5
8, 6
9, 7

So if you graph these points it will look like a V coming down to the point (2, 0). The slopes will be -1 and 1 respectively for either side of the V.

If you've done it correctly it will look like the attached graph.

Answer 4

You're right on that the lines mean absolute value, so thus y is always going to be non-negative. The graph of absolute value looks like a "V". You can basically just graph 2 lines:

y = x -2 (for x >= 2), and
y = - (x - 2) for (x < 2)

Hope this helps!

Answer 5

Okay, several answers are helpful and even correct but so that you will understand more fully, please do the following. Get out the graph paper and draw your X and Y axii. Now, substitute real values both positive and negative for 'X' and perform the arithmetic operation and then change all to the absolute value (positive value of result of arithmetic ops). Now graph all the X,Y points you have just calculated. Maybe this will help you understand. Some points are: X0, Y2; X2,Y0; X4, Y2; X-2,Y4. Okay, enough hints. Do more for yourself. Good luck.

Answer 6

The other answerer is wrong. Your answer will end up looking like 2 Vs, but they will both begin on the X-axis. One will have a turning point at (2,0) and the second one at (-2,0). The lines making up the V should be perpendicular to each other.

Answer 7

y = absolute value of (x-2)
Your y value on your graph will always be zero or positive, and will only be zero at the point where x = 2

You will have two lines headed upward from that point (2,0)

Answer 8

the market value of a home is $ 48,000 and the rate of assessment is 45%. the tax rate is 52 mills $52per $1000. what is the yearly real estate tax?

Answer 9

it means absolute value, so u have 2 equations from this

x-2 = y
x-2 = -y

Answer 10

this is simple. all you need to do is move the function over to the right 2, then you do an absolute value function(up one over one to the left and up one over one to the right).