How to input a problem

Questions
1

Hi, i don’t know how to input this problem in Wolfram Alpha:
I can upload an image. but how as text?

Is it continuous?

3.PNG

2

I do not use Wolfram Alpha, but I think Wolfram alpha can understand the Wolfram language, and if so, try

   f[x_] := Piecewise[{{10 - x, -1 <= x <= 3}, {x^2 - 2, 3 < x <= 4}, {0, True}}]

The above works ok in Mathematica (which uses the Wolfram language).

3

Hi Nasser M. Abbasi, thank you very much…

didnt work at first i tweak it a bit … but i stay in darkness, i have the next answers, which one is the correct?:

a.PNG
a.PNG709×394 15.2 KB

b.PNG
b.PNG679×654 23.9 KB

OR

Thanks again

4

it depends on the domain. Between -1 and +4, the function is continuous (I think of a continuous function as one where I do not have to take my hand off the paper when I draw it). But outside the above domain, it is not. Since it is not even defined there. So when you ask if a function is continuous, you have to also say over what range. May be Wolfram alpha has a command to also tell it the range?

The derivative of the function, however, is not continuous, since there is a jump at x=3.

5

I see, Thank yo very much Nasser.