Question

The hourly wage increase each employee receives each year depends on their number of years of service. Every three years of service means an increase of $0.50 per hour. So, employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour. Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00. Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour. And, employees of at least nine years, but less than twelve years receive an increase of $2.00. Write a function to represent this scenario. This function is a step function.
True or False

Answer 1

The answer is true im 90% sure

Answer 2

Answer:

The function represents this scenario is:

$\left\{\begin{matrix}0.5, & if & 0\leq x< 3\\ 1, & if & 3\leq x< 6 \\ 1.5, & if & 6\leq x< 9\\ 2, & if & 9\leq x< 12\end{matrix}\right.$

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:

$\left\{\begin{matrix}0.5, & if & 0\leq x< 3\\ 1, & if & 3\leq x< 6 \\ 1.5, & if & 6\leq x< 9\\ 2, & if & 9\leq x< 12\end{matrix}\right.$

Step function is the is a piece wise function includes all constant piece.

For example: $\left\{\begin{matrix}x+2 & x\leq -1\\ 1 & x> 1 \end{matrix}\right.$

The obtained function is also a piece wise function includes all constant piece.

Hence, it is true that function is a step function.