Determine whether each equation defines y as a function of x. y = 6 -x²

검증된 단계별 안내

Recall the definition of a function: for each input value of x, there must be exactly one output value of y.

Look at the given equation: \(y = 6 - x^{2}\).

For any value of x, calculate the right side \(6 - x^{2}\) to find the corresponding y value.

Since squaring x (\(x^{2}\)) always gives a non-negative result and subtracting it from 6 gives a unique y for each x, there is only one y for each x.

Therefore, the equation defines y as a function of x because each x corresponds to exactly one y.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

55s

도움이 되었나요?

주요 개념

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

Definition of a Function

A function is a relation where each input (x-value) corresponds to exactly one output (y-value). This means for every x, there is only one y. Understanding this helps determine if an equation defines y as a function of x.

Evaluating Equations for Function Criteria

To check if an equation defines y as a function of x, substitute values of x and see if y has a unique value. If each x produces only one y, the equation represents a function.

Quadratic Functions and Their Graphs

The equation y = 6 - x² is a quadratic function, which graphs as a parabola opening downward. Since for each x there is only one y, quadratic equations like this define y as a function of x.

Determine whether each equation defines y as a function of x. y = 6 -x2