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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2:26 minutes

Problem 65

Textbook Question

For each function, find (a) ƒ(2) and (b) ƒ(-1). See Example 7.

Verified step by step guidance

Identify the function \( f(x) \) given in the problem.

To find \( f(2) \), substitute \( x = 2 \) into the function \( f(x) \).

Simplify the expression obtained after substituting \( x = 2 \) to find \( f(2) \).

To find \( f(-1) \), substitute \( x = -1 \) into the function \( f(x) \).

Simplify the expression obtained after substituting \( x = -1 \) to find \( f(-1) \).

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Key Concepts

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

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. For example, if ƒ(x) = 2x + 3, then to find ƒ(2), you replace x with 2, resulting in ƒ(2) = 2(2) + 3 = 7. This process is fundamental in understanding how functions behave at particular points.

Domain of a Function

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. Understanding the domain is crucial when evaluating functions, as certain inputs may lead to undefined outputs, such as division by zero or taking the square root of a negative number.

Example Reference

Referring to an example, such as Example 7 in this context, provides a model for solving similar problems. Examples typically illustrate the steps taken to evaluate functions or apply specific concepts, helping students grasp the methodology and apply it to their own evaluations effectively.