How do you obtain the graph of y=−3f(x)y=-3f\left(x\right)y=−3f(x) from the graph of y=f(x)y=f\left(x\right)y=f(x)?

Ch. 1 - Functions

Briggs - Calculus: Early Transcendentals 3rd Edition

Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Briggs 3rd Edition

Ch. 1 - Functions

문제 1.2.10

1장, 문제 1.2.10

How do you obtain the graph of $y=-3f$\left$(x$\right$)$ from the graph of $y=f$\left$(x$\right$)$ ?

검증된 단계별 안내

Start with the graph of y = f(x). This is your original function graph.

The transformation y = -3f(x) involves two operations: a vertical reflection and a vertical stretch.

First, apply a vertical reflection across the x-axis. This changes the graph of y = f(x) to y = -f(x), flipping it upside down.

Next, apply a vertical stretch by a factor of 3. This means you multiply all y-values of the graph by 3, making the graph taller by stretching it away from the x-axis.

Combine these transformations to obtain the final graph of y = -3f(x), which is the vertically stretched and reflected version of the original graph y = f(x).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

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

Function Transformation

Function transformation refers to the process of altering the graph of a function through various operations, such as shifting, stretching, or reflecting. In this case, the transformation involves multiplying the function f(x) by -3, which results in a vertical stretch by a factor of 3 and a reflection across the x-axis.

Vertical Stretch and Reflection

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller. A reflection across the x-axis flips the graph upside down. The transformation y = -3f(x) combines both effects: it stretches the graph of f(x) vertically by a factor of 3 and reflects it over the x-axis.

Graphing Techniques

Graphing techniques involve methods for accurately plotting the transformations of functions. To graph y = -3f(x), one can start with the original graph of y = f(x), apply the vertical stretch by multiplying the y-values by 3, and then reflect the resulting points across the x-axis to obtain the final graph.

How do you obtain the graph of y=−3f(x)y=-3f\(\left\)(x\(\right\))y=−3f(x) from the graph of y=f(x)y=f\(\left\)(x\(\right\))y=f(x)?

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Function Transformation

Vertical Stretch and Reflection

Graphing Techniques

How do you obtain the graph of $y=-3f\(\left\)(x\(\right\))$ from the graph of $y=f\(\left\)(x\(\right\))$ ?