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Can you explain the notation? Is the first one f'(x)=sin(πx)?

I mean, is it the first derivative, or is it just function 1, 2, and 3?

also, what is the notation in the final question? I see f(x)=sin(πx), x0

Hi it is function 1, function 2 and function 3. For part b what i meant was f(x)=sin(piX) , x <-3

Sorry for part b i meant that f(x)={ sin(pix) x <-3 , Ix+2I -3 less than or equal to x < less than or equal to 0, 1+e^-x x>0

Have you answered the question? If so where is it ? I can not see it for some reason. Thanks

That is the standard sine curve, period 2, amplitude from -1 to 1

function 2 is the regular absolute value plot, shifted 2 to the left.

y=2+e^-x has an asymptote at y=1, crosses the y-axis at y=2, and quickly ascends to the left.

As for the piecewise function. You simply take the pieces and put them together.

It is ugly and does not connect, but it is a function.

By the way, my computer has been unavailable for the last couple of days. My apologies for the delay. I hope the answer is still in time.