91Ó°ÊÓ

When we talk about functions, two essential concepts are the domain and range.
The domain is the set of all possible input values for the function. In this case, it represents the number of years the employee worked at the corporation. Since the employee worked for 10 years, the domain is from 0 to 10 years, inclusive. We can express this as: \[0 \leq t \leq 10\].

The range, on the other hand, is the set of all possible output values. Here, the output is the salary, which was constant at \(\$25000\) per year. This means that no matter what year you look at within the domain, the salary remains \(\$25000\). Thus, the range is: \[\{25000\} \].

Understanding domain and range helps in accurately describing the behavior of a function over its entire span of interest.

Graphing a function provides a visual representation that can make the relationship between variables clearer.
To graph a function, we plot points that satisfy the function’s equation and then connect these points in a meaningful way.

For the salary function \(S(t) = 25000\), we know that the salary does not change with time. This means that for every value of \(t\) within the domain, the salary \(S(t)\) is always \(25000\).

To graph this, you'll need:

• An x-axis representing time in years.
• A y-axis representing salary in dollars.
• Plot points from \(t = 0\) to \(t = 10\) on the x-axis, each paired with the y-value \(25000\).

Connect these points, and you'll get a horizontal line, providing a visual confirmation that the salary does not change with time.

A horizontal line graph is one of the simplest forms of graphing a function. When you have a constant function, like \(S(t) = 25000\), its graph will always be a horizontal line.

This is because the output (salary) remains the same regardless of the input (time). So, every point on the line will have the same y-value.

Steps to draw a horizontal line graph:

• Draw your x-axis (time) and y-axis (salary).
• Mark the domain on the x-axis (0 to 10 years).
• Draw a horizontal line at the y-value corresponding to the salary (25000 dollars).

Label the axes to make the graph understandable at a glance. This simple graphical representation efficiently conveys that the salary did not change over the 10 years of employment.