Pc Functions Piecewise Defined

These are functions that are defined differently on different parts of the domain.

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− x , x < 0 f ( x) =  2 x , x ≥ 0

This means for x’s less than 0, put them in f(x) = -x but for x’s greater than or equal to 0, put them in f(x) = x2

What Whatdoes doesthe thegraph graph of of f(x) f(x) ==-x x2 look look like? like? Rememberyy==f(x) f(x)so solets let’s Remember graphyy==x-2 xwhich whichisisaasquare line of graph slope –1(parabola) and y-intercept 0. function Since Sincewe weare areonly only supposed supposedto tograph graphthis thisfor for xx< ≥ 0, we’ll only stop keep the graph the right at x = half 0. of the graph.

This then is the graph for the piecewise function given above.

2 x + 5, − 3 ≤ x < 0  f ( x ) = − 3, x=0 − 5 x , x>0 

For For 00the thefunction function Forxx x>= values between isvalue to be –3supposed andis0supposed graph the to along be so line plot ythe = - 5x. line–3 ythe = 2x + 5. point (0, -3)

Since you know this the graph graph is is aa piece of a line, you can just plug in each 0 to see endwhere value to to start get the the line and endpoints. then count af(-3) – 5 =slope. -1 and f(0) = 5

So this the graph of the piecewise function

solid dot for "or equal to"

open dot since not "or equal to"