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

Previous problemNext problem

1:10 minutes

Problem 62

Textbook Question

For each function, find (a) ƒ(2) and (b) ƒ(-1). See Example 7.ƒ = {(2, 5), (3, 9), (-1, 11), (5, 3)}

Verified step by step guidance

Identify the given function as a set of ordered pairs: \( \{(2, 5), (3, 9), (-1, 11), (5, 3)\} \).

To find \( f(2) \), locate the ordered pair where the first element is 2. In this case, it is \((2, 5)\).

The value of \( f(2) \) is the second element of the ordered pair \((2, 5)\), which is 5.

To find \( f(-1) \), locate the ordered pair where the first element is -1. In this case, it is \((-1, 11)\).

The value of \( f(-1) \) is the second element of the ordered pair \((-1, 11)\), which is 11.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

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

Function Definition

A function is a relation that assigns exactly one output for each input from a given set. In this context, the function ƒ is represented as a set of ordered pairs, where the first element is the input (domain) and the second element is the output (range). Understanding this definition is crucial for determining the outputs for specific inputs.

Evaluating Functions

Evaluating a function involves substituting a specific input value into the function to find the corresponding output. For example, to find ƒ(2), one must look for the ordered pair in the function where the first element is 2 and then identify the second element as the output. This process is essential for solving the given problem.

Ordered Pairs

Ordered pairs are pairs of numbers that represent a point in a two-dimensional space, where the first number indicates the x-coordinate (input) and the second number indicates the y-coordinate (output). In the function ƒ, each ordered pair provides a direct mapping from an input to its output, which is fundamental for evaluating the function at specific values.