교과서 질문
In Exercises 53–58, f and g are defined by the following tables. Use the tables to evaluate each composite function. (go f) (-1)
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
3장, 문제 55
Use the vertical line test to identify graphs in which y is a function of x.
검증된 단계별 안내1
Recall that the vertical line test is used to determine if a graph represents a function. The test states that if any vertical line intersects the graph at more than one point, then the graph does not represent a function.
Look at the graph and imagine drawing vertical lines (lines parallel to the y-axis) at various x-values across the domain of the graph.
Check if any vertical line crosses the red curve more than once. If no vertical line intersects the curve at more than one point, then y is a function of x.
In this graph, observe that for every x-value, the vertical line intersects the curve at exactly one point, meaning each x-value corresponds to only one y-value.
Therefore, based on the vertical line test, this graph represents y as a function of x.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
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주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Vertical Line Test
The vertical line test is a visual method used to determine if a graph represents a function. If any vertical line drawn through the graph intersects it at more than one point, the graph does not represent a function. This test ensures that each input (x-value) has only one output (y-value).
추천 영상:
가이드 코스
06:49
The Slope of a Line
Definition of a Function
A function is a relation where each input corresponds to exactly one output. In terms of graphs, this means for every x-value, there is only one y-value. Understanding this definition is crucial to applying the vertical line test correctly.
추천 영상:
5:57Graphs of Common Functions
Interpreting Graphs on the Cartesian Plane
Graphs on the Cartesian plane plot pairs of x and y values. Being able to read and analyze these graphs helps in identifying whether the relation shown is a function. Recognizing the shape and behavior of the curve aids in applying tests like the vertical line test.
추천 영상:
가이드 코스
05:10Graphs & the Rectangular Coordinate System
관련 실천
교과서 질문
Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y² – 10x – 6y – 30 = 0
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교과서 질문
Graph each equation in a rectangular coordinate system. f(x) = 1
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교과서 질문
In Exercises 55–59, use the graph of to graph each function g.
g(x) = f(x + 2) + 3
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교과서 질문
In Exercises 51–54, graph the given square root functions, f and g, in the same rectangular coordinate system. Use the integer values of x given to the right of each function to obtain ordered pairs. Because only nonnegative numbers have square roots that are real numbers, be sure that each graph appears only for values of x that cause the expression under the radical sign to be greater than or equal to zero. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = √x (x = 0, 1, 4, 9) and g (x) = √(x + 2) (x = = −2, −1, 2, 7)
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교과서 질문
Begin by graphing the standard quadratic function, f(x) = x². Then use transformations of this graph to graph the given function. g(x) = (x − 2)²
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