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Ch. 1 - Functions
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Briggs 3rd EditionCh. 1 - Functions문제 14c
1장, 문제 14c

Use the graph of ff in the figure to plot the following functions.
<IMAGE>
y=f(x−2)y=f\(\left\)(x-2\(\right\))

검증된 단계별 안내
1
Identify the transformation involved in the function y = f(x - 2). This represents a horizontal shift of the graph of f(x) to the right by 2 units.
Examine the key points on the original graph of f(x). These points will help in accurately shifting the graph.
Shift each key point of the graph of f(x) 2 units to the right. For example, if a point on f(x) is (a, b), it will become (a+2, b) on the graph of y = f(x - 2).
Redraw the graph using the shifted points to represent y = f(x - 2). Ensure that the shape and orientation of the graph remain unchanged, only the position is altered.
Verify the transformation by checking that all points have been shifted correctly and the overall graph maintains the same features as the original, just translated horizontally.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
4m
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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 the context of the question, the function y = f(x - 2) represents a horizontal shift of the original function f by 2 units to the right. Understanding how these transformations affect the graph is crucial for accurately plotting the new function.
추천 영상:
가이드 코스
5:25
Intro to Transformations

Graphing Functions

Graphing functions involves plotting points on a coordinate system to visually represent the relationship between the input (x-values) and output (y-values) of a function. This process requires knowledge of the function's behavior, including its intercepts, asymptotes, and overall shape. In this question, students must apply their graphing skills to represent the transformed function based on the original graph of f.
추천 영상:
가이드 코스
5:53
Graph of Sine and Cosine Function

Horizontal Shifts

Horizontal shifts occur when a function is modified by adding or subtracting a constant to the input variable. Specifically, in the function y = f(x - 2), the '-2' indicates a shift to the right by 2 units. This concept is essential for understanding how the graph of the function changes position on the x-axis, which directly impacts the overall appearance of the graph.
추천 영상:
가이드 코스
5:28
Horizontal Parabolas
관련 실천
교과서 질문

If ƒ(x) = √x and g(x) = x³-2 and , simplify the expressions (ƒ o g) (3), (ƒ o ƒ) (64), (g o ƒ) (x) and (ƒ o g) (x)

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교과서 질문

The parabola y=x²+1 consists of two one-to-one functions, g₁(x) and g₂(x). Complete each exercise and confirm that your answers are consistent with the graphs displayed in the figure. <IMAGE>


Find formulas for g₁((x) and g₁⁻¹(x). State the domain and range of each function.

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교과서 질문

Find functions ƒand g such that ƒ(g(x)) = (x² +1)⁵ . Find a different pair of functions ƒ and g that also satisfy ƒ(g(x)) = (x² +1)⁵  

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교과서 질문

Use the graphs of ƒ and g in the figure to determine the following function values. y = f(x) ; y=g(x) <IMAGE>



a. (ƒ o g ) (2)

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교과서 질문

Evaluate cos⁻¹(cos(5π/4)).

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교과서 질문

Use the graph of ff in the figure to plot the following functions.

<IMAGE>

y=f(x−1)+2y=f\(\left\)(x-1\(\right\))+2

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