Determine whether each function graphed or defined is one-to-one. y = -1 / x+2

검증된 단계별 안내

Identify the given function: \(y = -\frac{1}{x} + 2\).

Recall that a function is one-to-one if each \(y\)-value corresponds to exactly one \(x\)-value, meaning the function passes the Horizontal Line Test.

Analyze the function's behavior: since \(y = -\frac{1}{x} + 2\) is a transformation of the reciprocal function \(y = \frac{1}{x}\), consider how the negative sign and the +2 shift affect its graph.

Check if the function is strictly increasing or strictly decreasing on its domain, because strictly monotonic functions are one-to-one.

Conclude by determining if any horizontal line intersects the graph more than once, which would indicate the function is not one-to-one.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

One-to-One Function

A function is one-to-one if each output corresponds to exactly one input, meaning no two different inputs produce the same output. This property ensures the function has an inverse that is also a function.

Horizontal Line Test

The horizontal line test is a visual method to determine if a function is one-to-one. If any horizontal line intersects the graph more than once, the function is not one-to-one.

Rational Functions and Their Graphs

Rational functions are ratios of polynomials, often with vertical and horizontal asymptotes. Understanding their shape helps analyze behavior and determine if they pass the horizontal line test for one-to-one properties.