Functions Help

[shaylee112]

THe question states which of the following are functions?

a. f(x) = 2 if x>1
f(x) = -1 otherwise

b. f(x) = 5 if x >0
f(x) =-5 if x<0
f(x) =5 or -5 if x =0

c. f(x) = 10/x


these are hard to me compared to the ones in the reading and examples I had I don't understand these can someone help explain these? Thanks

 

[Unco]

Try graphing them: if there is a point where one input (x) gives more than one output (e.g. two y values) then it is not a function. You can view this as a function must not cross a vertical line more than once.

 

[shaylee112]

how would I do that when I don't understand how to get the points to graph?

 

[Unco]

We can change that...

f(x) = 2 if x>1
f(x) = -1 otherwise

ie. The graph is the horizontal line y = 2 when x>1 and the horizontal line y=-1 when x\(\displaystyle \leq1\):

                 /|\ y
                  |
                  |
                2-|   o-------------- y=2 begins where x=1 
                  |                        but excludes x=1 so 
                  |---+-------------> x     we draw a hole.
                  |   1 
      ------------|---* y=-1 begins where
                              x=1 and includes x=1

We cannot draw a vertical line where the two graphs cross it. At x=1, there is only one output: y=-1 because the y=2 graph excluded x=1.

Are we on the same wavelength?