91Ó°ÊÓ

An ordered pair consists of two elements arranged in a specific order, usually representing a point in a two-dimensional space. It is commonly expressed as

• (x, y)

In the context of functions, ordered pairs are used to show the relationship between the input and output values of a function. The first element, x, represents the input value while the second element, y, represents the output value obtained by substituting x into a function.
For the function given in the exercise:

• x is substituted into the function to find the corresponding y value.

To determine if an ordered pair is a solution to a function, the calculated output value must match the y-value in the pair. If it matches, it confirms that point (x, y) lies on the graph of the function, validating the ordered pair as a solution.

Algebra is a branch of mathematics that uses symbols such as letters and numbers to represent numbers and express mathematical relationships. It allows us to solve equations and find unknown values. Functions form an essential part of algebra as they describe the relationship between variables in the form of equations.
A key feature of algebra is manipulating equations to evaluate expressions, which involves tasks like addition, subtraction, multiplication, or division of numbers and variables.
In the example provided, algebra is used by:

• Identifying the function: Recognizing the relationship or rule (in this case, subtracting 4 from x).
• Substituting: Replacing x with a given numeric value (12 in the exercise).
• Simplifying: Performing subtraction to find the function's output (8, our result).

This step-by-step approach shows the power of algebra in solving and understanding mathematical problems.

The substitution method involves replacing a variable in an equation or function with a specific number to compute an expression's output. This technique is handy in function evaluation when determining whether a given ordered pair is a solution.
To use substitution effectively:

• Identify the variable to substitute in the function equation.
• Replace this variable with the given value from your ordered pair.
• Solve or simplify the equation to find the output value.

In the given exercise, by substituting x with 12 in the function, you derive an outcome of 8, which matches the ordered pair's y-value. This match confirms that when x equals 12, y equals 8, verifying the ordered pair (12, 8) as a solution.