Answer: The below figure shows the graph of f(x).
Explanation: Given function, [tex]f(x)=\begin{cases}5 & \text{ if } x<-5 \\ -2 & \text{ if } -5\leq x\leq 6 \\ 1 & \text{ if } x>6 \end{cases}[/tex]
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 [tex]-5\leq x\leq 6[/tex], 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).
Answer:
Refer the attachment.
Step-by-step explanation:
Given piece wise-defined function,
[tex]f(x)=\left\{\begin{matrix} -5 & if\ x<-5 \\ -2 & if \ -5\leq x\leq 6 \\ 1& if \ x>6 \end{matrix}\right.[/tex]
We have to graph the given piece wise-defined function,
[tex]f(x)=\left\{\begin{matrix} -5 & if\ x<-5 \\ -2 & if \ -5\leq x\leq 6 \\ 1& if \ x>6 \end{matrix}\right.[/tex]
Consider the given function ,
[tex]f(x)=\left\{\begin{matrix} -5 & if\ x<-5 \\ -2 & if \ -5\leq x\leq 6 \\ 1& if \ x>6 \end{matrix}\right.[/tex]
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.
