Piece-wise functions and discontinuity

[stinajeana]

Hello!

.Hello! i'm having trouble understanding piece-wise functions and discontinuity. I don't want the answer I just want to know what I have to do when there is a "3" instead of a polynomial.... usually I would just plug the number into x and that's it but what do I do when there's just a 3?! and what does it mean?

 

[chalaman1403]

Stinajeana.

When you have a function that is constant, this is \(\displaystyle f(x) = c\) it just doesn't depend on x, the outcome is always 3, it doesn't matter if it is piece wise or not, you just get 3 all the time, beacuse it doesn't depend on x. It is a "polynomial" of degree 0.
Regards,
Damián Vallejo

 

[stapel]

i'm having trouble understanding piece-wise functions and discontinuity.... I just want to know what I have to do when there is a "3" instead of a polynomial.... and what does it mean?

If you plug in x = -1, then you get y = 3.
If you plug in x = -0.9, then you get y = 3.
If you plug in x = -0.8, then you get y = 3.
If you plug in x = -0.7, then you get y = 3.
If you plug in x = -0.6, then you get y = 3.
If you plug in x = -0.5, then you get y = 3.
If you plug in x = -0.4, then you get y = 3.
If you plug in x = -0.3, then you get y = 3.
If you plug in x = -0.2, then you get y = 3.
If you plug in x = -0.1, then you get y = 3.
If you plug in x = 0, then you get y = 3.

Plot these points. What sort of line do you get? What value slope does this sort of line have?

This part of the piecewise function is nothing but a really boring horizontal line.