Question

Which graph represents the piecewise-defined function?

y=⎧⎩⎨⎪⎪5   if  x<−5−2   if  −5≤x≤61    if  x>6

Answer 1

Refer the attachment.

Explanation:

Given piece wise-defined function,

`f(x)=\left\{\begin{matrix} -5 & if\ x<-5 \\  -2 & if \ -5\leq x\leq 6  \\  1&  if \ x>6 \end{matrix}\right.`

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

`f(x)=\left\{\begin{matrix} -5 & if\ x<-5 \\  -2 & if \ -5\leq x\leq 6  \\  1&  if \ x>6 \end{matrix}\right.`

Consider the given function ,

`f(x)=\left\{\begin{matrix} -5 & if\ x<-5 \\  -2 & if \ -5\leq x\leq 6  \\  1&  if \ x>6 \end{matrix}\right.`

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.