Answer:
The function represents this scenario is:
[tex]\left\{\begin{matrix}0.5, & if & 0\leq x< 3\\ 1, & if & 3\leq x< 6 \\ 1.5, & if & 6\leq x< 9\\ 2, & if & 9\leq x< 12\end{matrix}\right.[/tex]
It is true that function is a step function.
Step-by-step explanation:
Consider the provided information.
Let x is the number of years of service.
For less than use the inequality < and for at least use the inequity ≤.
It is given that employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour.
Which can be written as:
0.05 if 0 ≤ x < 3
Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00.
This can be written as:
1.00 if 3 ≤ x < 6
Employees that have been with the company for at least six years, but less than nine years, receive an increase of $1.50 per hour.
This can be written as:
1.50 if 6 ≤ x < 9
And, employees of at least nine years, but less than twelve years receive an increase of $2.00.
This can be written as:
2.00 if 9 ≤ x < 12
Hence, the function represents this scenario is:
[tex]\left\{\begin{matrix}0.5, & if & 0\leq x< 3\\ 1, & if & 3\leq x< 6 \\ 1.5, & if & 6\leq x< 9\\ 2, & if & 9\leq x< 12\end{matrix}\right.[/tex]
Step function is the is a piece wise function includes all constant piece.
For example: [tex]\left\{\begin{matrix}x+2 & x\leq -1\\ 1 & x> 1 \end{matrix}\right.[/tex]
The obtained function is also a piece wise function includes all constant piece.
Hence, it is true that function is a step function.
