How do you obtain the graph of y=f(x+2)y=f\left(x+2\right)y=f(x+2) 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

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Briggs 3rd Edition

Ch. 1 - Functions

문제 9

1장, 문제 9

How do you obtain the graph of $y=f$\left$(x+2$\right$)$ from the graph of $y=f$\left$(x$\right$)$ ?

검증된 단계별 안내

Understand that the expression y = f(x + 2) represents a horizontal transformation of the function y = f(x).

Recognize that adding a positive number inside the function's argument, such as x + 2, results in a horizontal shift to the left.

To graph y = f(x + 2), take each point (x, y) on the graph of y = f(x) and shift it 2 units to the left, resulting in the new point (x - 2, y).

Ensure that all points on the original graph are shifted consistently to maintain the shape of the graph.

Check the new graph to confirm that it accurately represents the function y = f(x + 2) by verifying a few key points and their transformations.

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 shifts, stretches, or reflections. In this case, the function y = f(x + 2) represents a horizontal shift of the original function y = f(x) to the left by 2 units. Understanding how these transformations affect the graph is crucial for accurately sketching or interpreting the new function.

Horizontal Shifts

Horizontal shifts occur when the input variable of a function is adjusted by adding or subtracting a constant. For the function y = f(x + 2), the addition of 2 inside the function's argument indicates a shift to the left. This concept is essential for predicting how the graph will move in relation to the original function.

Graphing Functions

Graphing functions involves plotting points on a coordinate plane to visually represent the relationship between the input (x) and output (y) values. To graph y = f(x + 2), one must first understand the original graph of y = f(x) and then apply the horizontal shift. This skill is fundamental in calculus for analyzing and interpreting functions.

How do you obtain the graph of y=f(x+2)y=f\(\left\)(x+2\(\right\))y=f(x+2) 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

Horizontal Shifts

Graphing Functions

How do you obtain the graph of $y=f\(\left\)(x+2\(\right\))$ from the graph of $y=f\(\left\)(x\(\right\))$ ?