Question

How do you graph `y= abs(x-1)`?

Answer 1

Use a calculator table

Explanation:

Honestly it's like `2*10^10` times easier to use a calculator but if you want the table version here it is:
First you should know what the equation actually does
The `-1` in the absolute value bars means the graph is going to shift one to the right and if it was `+1` the graph would shift to the left one.
If there is a number between `0 and 1` in the front of the absolute value bars the graph is going to get wider and any other number is going to make the graph smaller.
`y=.4|x|` smaller
`y=3|x|` wider
Also, if there is a number getting added or subtracted to the absolute value bars than the y axis is affected.
Any number that is added to the outside of the bars is going to make it rise that amount and vise versa for subtraction.
Lastly, if there is a negative in the very from of the equation than the graph gets flipped.
`y=|x|+3` up three
`y=|x|-3` down three

Now that you have all that down you can start picking points for you table.
I know that since the equation is `y=|x-1|` that it is going to move to the right one so the starting point is going to be `(1,0)`
After that you need to pick two numbers on opposite sides of that point to graph it.
Since the middle is at `(1,0)` pick `x` points like `-3` and `5`
Once you have your two points, plug them into the equation:
`y=|(-3)-1|`
`y=|-4|`
`y= 4`

And

`y=|(5)-1|`
`y=|4|`
`y=4`

Now you know that `(1,0), (-3,4), and (5,4)`
To plot just follow the coordinates
Just a tip, anything with absolute value bars is going to be a V so if it's not you did something wrong.

Answer 2

Please read the explanation.

Explanation:

`color(red)(y=|x-1|`

This function is an Absolute Value Function.

An absolute value function is a function that contains an algebraic expression within absolute value symbols `color(blue)(|" "|`.

Please remember that the absolute value of a number is its distance from 0 on the number line.

So the absolute value of both `color(blue)((+6)` and `color(blue)((-6)` are `color(green)("6 units"` from zero (0) on the number line.

To graph an absolute value function, choose several values of x and find some ordered pairs.

Plot the points on a coordinate plane and connect them.

The Parent function `color(green)(y=|x|` is included in the graph for comparison.

You can understand how the graph of `y=|x-1|` differs from the graph of `y=|x|`.

Use the function `color(brown)(g(x)=f(x-h)`

When `h>0`, the graph of `f(x)` is translated `"h units"` to the right to obtain `g(x)`.

Hence, notice that the vertex is now `(1,0)` for the our function `color(red)(y=|x-1|`.

Hope it helps.