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A constant function is a type of function where the output value remains the same regardless of the input value. This means if you have a function like \(f(x) = 5\), no matter what you substitute for \(x\), the result is always 5. Constant functions are easy to identify because they are written as \(f(x) = c\), where \(c\) is a constant number.
For example, in our exercise, we have \(f(x) = 5\). This '5' is the constant output value we get for any input. Constant functions do not change their values, making them quite predictable and simple to understand.
The graph of a constant function is always a straight horizontal line. Understanding this makes graphing them easier, as you only need to identify the y-value where the horizontal line should be drawn.

The domain and range of a function are essential concepts in understanding how functions behave.
The domain of a function consists of all possible input values (x-values) that the function can accept. For example, in constant functions like \(f(x) = 5\), the domain is all real numbers since we can plug in any number into the function. This is written as \(\text{Domain}: (-\infty, \infty)\).
The range of a function is the set of all possible output values (y-values) of the function. Since a constant function always outputs the same value, the range is simply that value. In our example, \(f(x) = 5\) always outputs 5, so the range is \(\text{Range}: \{5\}\).
In summary, for constant functions:

• The domain is all real numbers.
• The range is the single value that the function outputs.

In the context of graphing functions, a horizontal line is one that goes straight across the graph from left to right at a constant y-value.
For a constant function like \(f(x) = 5\), the graph is a horizontal line that crosses the y-axis at y = 5. This is because the output value does not change and remains constantly equal to 5. Drawing this line is straightforward: simply draw a line parallel to the x-axis that passes through the point where y equals 5.
Horizontal lines are simple yet fundamental when learning to graph and understand functions. They clearly illustrate the behavior of constant functions and make it easier to grasp the concepts of domain and range.
To summarize:

• A horizontal line graph represents a function with a constant output value.
• It intersects the y-axis at the given constant value, in this case, 5.
• It visually shows that for all x-values (the domain), the output (the range) remains the same.