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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 14e
1장, 문제 14e

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

검증된 단계별 안내
1
Identify the transformation components in the function y = f(x-1) + 2. The function involves a horizontal shift and a vertical shift.
Recognize that the expression (x-1) indicates a horizontal shift. Specifically, f(x-1) represents a shift of the graph of f(x) to the right by 1 unit.
Understand that the '+2' outside the function indicates a vertical shift. This means that after shifting the graph to the right, you will move it up by 2 units.
Start by taking each point on the original graph of f(x) and apply the horizontal shift. Move each point 1 unit to the right.
After applying the horizontal shift, apply the vertical shift by moving each of the new points 2 units up. Plot these new points to obtain the graph of y = f(x-1) + 2.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
5m
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주요 개념

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

Function Transformation

Function transformation refers to the changes made to the graph of a function through operations such as shifting, stretching, or reflecting. In the given equation, y = f(x - 1) + 2, the function f is shifted to the right by 1 unit and then raised vertically by 2 units. Understanding these transformations is crucial for accurately plotting the new function based on the original graph.
추천 영상:
가이드 코스
5:25
Intro to Transformations

Horizontal Shift

A horizontal shift occurs when a function is moved left or right along the x-axis. In the expression f(x - 1), the subtraction of 1 indicates a shift to the right by 1 unit. This concept is essential for determining how the input values of the function are altered, affecting the overall position of the graph.
추천 영상:
가이드 코스
5:28
Horizontal Parabolas

Vertical Shift

A vertical shift involves moving a function up or down along the y-axis. In the equation y = f(x - 1) + 2, the addition of 2 results in a vertical shift upwards by 2 units. This concept helps in understanding how the output values of the function are adjusted, which is necessary for accurately plotting the transformed function.
추천 영상:
가이드 코스
5:30
Foci and Vertices of an Ellipse
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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

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

<IMAGE>

y=f(x−2)y=f\(\left\)(x-2\(\right\))

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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>


b. g (ƒ (2))

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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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