An equation that defines y as a function of x is given. (b) Find ƒ(3). x-4y=8

Key Concepts

Functions

A function is a relation that assigns exactly one output (y) for each input (x). In this context, the equation defines y as a function of x, meaning for every value of x, there is a corresponding value of y. Understanding functions is crucial for evaluating specific inputs, such as finding ƒ(3).

Solving Equations

Solving equations involves manipulating the equation to isolate the variable of interest. In this case, we need to rearrange the equation x - 4y = 8 to express y in terms of x. This process is essential for determining the function and subsequently finding the value of ƒ(3).

Substitution

Substitution is the process of replacing a variable in an expression or equation with a specific value. Once the function is defined, substituting x = 3 into the function allows us to calculate the corresponding value of y, which is the desired output for ƒ(3). This step is critical for evaluating the function at a given point.