2 Attachment(s)

Identify the discontinuity. f'(x) for the f(x).

Attachment 29630

I did graph the inequality.Attachment 29631

Is see the y intercept at 5 and what looks like opposite slopes. I replaced a with 5. The notation of question e):

$\displaystyle f'(x)$ for the $\displaystyle f(x)$ in d)

is a little bit confusing to me. If I am correct the $\displaystyle f'(x)=-1$ and $\displaystyle f'(x)=1$ for the function in d)

I am trying to determine how to graph:

$\displaystyle f'(x)$ for the $\displaystyle f(x)$ in d)

Thanks in advance...

Re: Identify the discontinuity. f'(x) for the f(x).

Part d is a v shape Just the top part of your graph. Ofcourse, you don't know what the value of 'a' is so you don't know if the vertex is above or below the x axis, but you do know it is a V

When x>0 the gradient is +1, when x<0 the gradient is -1

What happens when x=0? The graph is not defined. There is no f(x) value when x=0, f(x) is undefined when x=0 so f(x) is discontinuous when x=0

You show this on a graph by putting an open circle around this point (0,a)

Now when x>0 f'(x)=1 This is just a line horizontal to the x axis starting at (0,1) x=0 is not included so it will start with an open circle

And, when x<0 f'(x)=-1 This is just a line horizontal to the x axis starting at (0,-1) x=0 is not included so it will start with an open circle

So f'(x) is discontinuous at x=0 and the two halves start in very different places.

(Sorry, I don't know what the words are for different types of discontinuity)