교과서 질문
In Exercises 19–32, find the (a) domain and (b) range.
𝔂 = tan(2x - π)
342
views
Ch. 1 - Functions
Hass15th EditionThomas' CalculusISBN: 9780137616077
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. 1 - Functions155
- Ch. 2 - Limits and Continuity240
- Ch. 3 - Derivatives337
- Ch. 4 - Applications of Derivatives293
- Ch. 5 - Integrals41
- Ch. 6 - Applications of Definite Integrals25
- Ch. 7 - Transcendental Functions489
- Ch. 8 - Techniques of Integration398
- Ch. 9 - First-Order Differential Equations60
- Ch. 10 - Infinite Sequences and Series119
- Ch. 11 - Parametric Equations and Polar Coordinates58
1장, 문제 1.37.1
In Exercises 37 and 38, write a piecewise formula for the function.
<IMAGE>
검증된 단계별 안내1
Identify the different intervals on the x-axis where the function changes its behavior. This is typically where the graph has breaks or changes direction.
For each interval, determine the formula that represents the function. This involves analyzing the graph and identifying the type of function (e.g., linear, quadratic) that fits the segment.
Write the piecewise function using the identified formulas for each interval. Use the format: f(x) = {formula1 for interval1, formula2 for interval2, ...}.
Ensure that the conditions for each interval are clearly defined, using inequalities to specify where each formula applies.
Double-check the continuity and endpoints of each interval to ensure the piecewise function accurately represents the graph across all specified intervals.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
4m도움이 되었나요?
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Piecewise Functions
A piecewise function is defined by different expressions based on the input value's range. Each 'piece' of the function applies to a specific interval of the domain. Understanding how to construct and interpret these functions is crucial for solving problems that involve different behaviors over different intervals.
추천 영상:
05:36
Piecewise Functions
Domain and Range
The domain of a function is the set of all possible input values, while the range is the set of all possible output values. For piecewise functions, it's essential to identify the domain for each piece to ensure the function is correctly defined over its entire range. This helps in writing accurate piecewise formulas.
추천 영상:
5:10Finding the Domain and Range of a Graph
Function Notation
Function notation involves expressing functions in a form like f(x) to denote the output of function f for input x. In piecewise functions, notation is used to specify different expressions for different intervals, often using conditions like 'if' or 'for' to clarify which expression applies to which part of the domain.
추천 영상:
04:22Sigma Notation
관련 실천
교과서 질문
In Exercises 9–16, determine whether the function is even, odd, or neither.
𝔂 = x⁵ - x³ - x
218
views
교과서 질문
Functions and Graphs
Find the natural domain and graph the functions in Exercises 15–20.
g(x) = √−x
348
views
교과서 질문
Shifting Graphs
The accompanying figure shows the graph of y = −x² shifted to four new positions. Write an equation for each new graph.
<IMAGE>
205
views
교과서 질문
In Exercises 19–32, find the (a) domain and (b) range.
____
𝔂 = -2 + √1 - x
409
views
교과서 질문
[Technology Exercise]
a. Graph the functions f(x) = 3/(x − 1) and g(x) = 2/(x + 1) together to identify the values of x for which
3/(x − 1) < 2/(x + 1)
b. Confirm your findings in part (a) algebraically.
207
views