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

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Start with the given equation: \(x - 4y = 8\).

Rewrite the equation to express \(y\) as a function of \(x\). To do this, isolate \(y\) on one side: subtract \(x\) from both sides to get \(-4y = 8 - x\).

Divide both sides of the equation by \(-4\) to solve for \(y\): \(y = \frac{8 - x}{-4}\).

Simplify the expression for \(y\): \(y = -2 + \frac{x}{4}\).

To find \(f(3)\), substitute \(x = 3\) into the function: \(f(3) = -2 + \frac{3}{4}\).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Function Definition

A function defines a relationship where each input x corresponds to exactly one output y. In this problem, y is expressed as a function of x, meaning for each x-value, there is a unique y-value that satisfies 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, or dividing terms, to express y explicitly in terms of x.

Evaluating the function at a specific value

Once y is expressed as a function of x, finding ƒ(3) means substituting x = 3 into the function and calculating the corresponding y-value. This step applies the function definition to a particular input.