Question

f(x)={x+3 if -2<=x< 1
9 if x=1
-x+2 ifx>1]

find the domain, intercepts and graph. Someone please help.

Answer 1

For the domain, look at which values of x the function is defined for.
There are 3 parts. -2 <= x < 1, x = 1, and x > 1
When you put them all together, you get:
The domain is x >= -2

Answer 2

Now you need to graph each part according to its domain.
The first part, f(x) = x + 3 has a y intercept of 3 and a slope of 1. This is a 45-degree (up from the horizontal) line going up to the right. This 45-degree segment goes from x = -2 to an open circle at x = 1.
At x = 1, y = 9. plca a closed circle there.
Then for the third part, start by plotting the line that has y-intercept 2 and slope -1, which is a 45-degree (down from the horizontal) line down to the right, but start the line only at x = 1 with an open circle on x = 1 and going to the right.