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

Verified step by step guidance

1. Start with the given equation: \(x - 4y = 8\).
2. To find \(f(3)\), we need to express \(y\) as a function of \(x\), so solve the equation for \(y\) in terms of \(x\).
3. Isolate the term with \(y\): subtract \(x\) from both sides to get \(-4y = 8 - x\).
4. Divide both sides by \(-4\) to solve for \(y\): \(y = \frac{8 - x}{-4}\).
5. Substitute \(x = 3\) into the expression for \(y\) to find \(f(3)\): \(f(3) = \frac{8 - 3}{-4}\).

Key Concepts

Function Definition

A function defines a relationship where each input x corresponds to exactly one output y. In this context, y is expressed as a function of x, meaning for each x-value, there is a unique y-value determined by the equation.

Solving for y in terms of x

To find y as a function of x, rearrange the given equation to isolate y on one side. This involves algebraic manipulation, such as adding, subtracting, multiplying, or dividing terms, to express y explicitly in terms of x.

Function Evaluation

Evaluating ƒ(3) means substituting x = 3 into the function and calculating the corresponding y-value. This step requires correctly substituting and simplifying the expression to find the output of the function at x = 3.