Question

How do you sketch the graph of `f(x)=(-x+1)` for `x<1` and `x-2` for `x>=1`?

Answer 1

I recommend using this free online graphing calculator:
https://www.desmos.com/calculator
I have explained how to graph by hand below.

Explanation:

I graphed the two equations with restrains here:
https://www.desmos.com/calculator/ciz5mrcl95

To sketch it on paper you would do as follows:
`color(red)(f(x) = (-x+1) {x<1})`:
1) Graph x using a table, but only use x = 1 and higher.
2) Because it is asking for all numbers `"greater than 1"`, put an open circle rather than a point at (1, 0). This shows that (1, 0) does not fulfill the equation, but every number after it does.

`color(green)(f(x) = (x-2) {x>=1}`
1) Graph x using a table, but only using x = 1 and higher.
2) Because it is asking for all numbers `"greater than or equal to 1"`, put a closed circle, a point, at (1, -1). This shows that (1, -1) does fulfill the equation and every number after it does, too.