Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

0. Review of College Algebra

Functions

Trigonometry

0. Review of College Algebra

Functions

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1:17 minutes

Problem 61

Textbook Question

For each function, find (a) ƒ(2) and (b) ƒ(-1). See Example 7.ƒ = {(-1, 3), (4, 7), (0, 6), (2, 2)}

Verified step by step guidance

Identify the given function as a set of ordered pairs: \( \{(-1, 3), (4, 7), (0, 6), (2, 2)\} \).

To find \( f(2) \), locate the ordered pair where the first element is 2. The second element of this pair is the value of \( f(2) \).

To find \( f(-1) \), locate the ordered pair where the first element is -1. The second element of this pair is the value of \( f(-1) \).

For part (a), check the pair \((2, 2)\) to determine \( f(2) \).

For part (b), check the pair \((-1, 3)\) to determine \( f(-1) \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Notation

Function notation is a way to represent a relationship between inputs and outputs. In this case, ƒ(x) indicates a function where 'x' is the input, and ƒ(x) is the corresponding output. The notation helps in identifying specific values of the function based on given pairs, such as ƒ(2) and ƒ(-1).

Ordered Pairs

Ordered pairs are a fundamental concept in functions, represented as (input, output). Each pair in the function ƒ = {(-1, 3), (4, 7), (0, 6), (2, 2)} indicates that for a specific input, there is a corresponding output. Understanding how to read and interpret these pairs is essential for finding the values of ƒ(2) and ƒ(-1).

Evaluating Functions

Evaluating a function involves substituting a specific input value into the function to find the output. For example, to find ƒ(2), you look for the ordered pair where the first element is 2 and determine the second element as the output. This process is crucial for solving the given problem and understanding how functions operate.