Which graph represents the piecewise-defined function? y=⎧⎩⎨⎪⎪5   if  x< −5−2   if  −5≤x≤61    if  x> 6

The below figure shows the graph of f(x).

Explanation: Given function,

Since, here three conditions are given,

In first case for values x<-5 , f(x)=5, so we get a line y=5 parallel to x-axis which passes through point (0,5).

In second case, for values  , f(x) =-2, so we get a line y=-2 parallel to x-axis which passes through point  (0,-2).

In third case, for values x>6, f(x)=1, so we get a line y=1 parallel to x-axis which passes through point (0,1).

Thus, these three lines make the piecewise-defined function f(x).

Refer the attachment.

Step-by-step explanation:

 Given piece wise-defined  function,

We have to graph the given piece wise-defined  function,

Consider the given function ,

We are given three conditions for the given function f(x)

Let f(x) equal to y.  

Case 1)

for value of  x < -5 ,the function takes the value 5.

that is  f(x) = 5,

so we get a line y = 5 parallel to x-axis for all values of x lying less than -5

Case 2)

for values  of -5≤  x ≤  6  the function takes value  -2

that is y = -2

so we get a line y = -2 parallel to x-axis. for all values of x lying between -5≤  x ≤  6

Case 3)

for values  of  x <  6  the function takes value  1

that is y = 1

so we get a line y = 1 parallel to x-axis for all values of x lying greater than 6.

Plot these we get the desired graph of  piece wise-defined function.

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step-by-step explanation:

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