## Shido88 2 years ago Graph piecewise function: p(x)={1/2x+1 if x cannot equal to 4 {2 if x = 4 State Domain and Range

1. zepdrix

|dw:1359425377274:dw|Basically what we want to do is - think of this as two different functions. It's the function \(p(x)=\dfrac{1}{2}x+1\) when `x is not 4`. And it's a different function \(q(x)=2\) when `x is 4`. So let's graph what I called `q` first, since that one is easy. c:

2. Shido88

ok :)

3. Shido88

so when x is not 4, that mean i can select x to be any number just dont pick 4 right ?

4. zepdrix

For all values of x, the function produces `2`. Normally that would look like a horizontal line like this,|dw:1359425605017:dw|But this function is only defined at x=4! So what we actually get is this.|dw:1359425634168:dw|

5. zepdrix

Oh sorry I was looking at the `x is 4` one first c: heh

6. Shido88

oh

7. zepdrix

I should delete that line on x=4.. I think that's confusing maybe.

8. Shido88

plz keep explaining...i got emergency but i brb thanks! :]

9. zepdrix

k

10. zepdrix

When `x is not 4` we have a linear function. It has a slope of 1/2, and a y-intercept of 1.

11. zepdrix

So it will cross the y-axis at y=1

12. zepdrix

|dw:1359425801166:dw|Remember, we can only graph this line where `x is not 4`. So when we get to that spot where x is 4, we draw an open circle to show that the line is not defined there.

13. zepdrix

The black dots on the left don't actually mean anything. I was just plotting a couple points so I could draw a line through them.

14. Shido88

@zepdrix what about the green dot ?

15. Shido88

so when x cannot equal to 4 then just don't include the 4

16. Shido88

oh i see now, the green dot is x=4 and it just a linear line

17. zepdrix

Yah the green dot is where the function is defined when `x=4`. It's like you have a straight line, with a hole in it at one spot. Think of a straight line, and one of the points broke off the line and fell to a spot below somewhere. The function is still defined at x=4, just in a different place, not along the line where you would normally think. Sorry late response :C site being slow tonight.