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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Lial 13th EditionCh. 2 - Graphs and Functions문제 28
3장, 문제 28

Determine whether each relation defines a function, and give the domain and range. See Examples 1–4.
Graph of a quadratic function with vertex at (8, -2) in college algebra functions chapter.

검증된 단계별 안내
1
Step 1: Determine if the relation is a function by using the vertical line test. If any vertical line intersects the graph at more than one point, the relation is not a function. For this graph, each vertical line intersects the parabola at exactly one point, so it defines a function.
Step 2: Identify the domain of the function. The domain consists of all possible x-values for which the function is defined. Since the parabola extends infinitely to the left and right, the domain is all real numbers, which can be written as \((-\infty, \infty)\).
Step 3: Identify the range of the function. The range consists of all possible y-values that the function can take. The vertex of the parabola is at (8, -2), and since the parabola opens downward, the maximum y-value is -2.
Step 4: Express the range using interval notation. Since the parabola opens downward and extends infinitely downward, the range includes all y-values less than or equal to -2, which is \((-\infty, -2]\).
Step 5: Summarize the findings: The relation is a function, the domain is all real numbers \((-\infty, \infty)\), and the range is \((-\infty, -2]\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
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주요 개념

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

Definition of a Function

A function is a relation where each input (x-value) corresponds to exactly one output (y-value). This means no vertical line intersects the graph more than once, ensuring each x has a unique y. The vertical line test is a common method to verify if a graph represents a function.
추천 영상:
5:57
Graphs of Common Functions

Domain of a Function

The domain is the set of all possible input values (x-values) for which the function is defined. For the given quadratic graph, the domain includes all x-values where the graph exists, typically all real numbers unless restricted by the graph's endpoints or breaks.
추천 영상:
3:51
Domain Restrictions of Composed Functions

Range of a Function

The range is the set of all possible output values (y-values) that the function can produce. For the parabola shown, the range includes all y-values from the vertex's minimum or maximum point (here, the vertex at (8, -2)) extending upwards or downwards depending on the parabola's direction.
추천 영상:
4:22
Domain & Range of Transformed Functions
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