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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2:29 minutes

Problem 67

Textbook Question

Use the graph of y = ƒ(x)to find each function value:(a) ƒ(-2) (b) ƒ(0) (c) ƒ(1) and (d) ƒ(4).See Example 7(d).

Verified step by step guidance

Step 1: Understand the problem. You are given a function y = ƒ(x) and need to find the values of the function at specific x-values: -2, 0, 1, and 4.

Step 2: Locate the graph of y = ƒ(x). This graph will show you the relationship between x and y values.

Step 3: For each x-value given in the problem, find the corresponding y-value on the graph.

Step 4: Specifically, look at the points on the graph where x = -2, x = 0, x = 1, and x = 4. The y-values at these points are ƒ(-2), ƒ(0), ƒ(1), and ƒ(4) respectively.

Step 5: Record the y-values you find for each x-value. These are the function values you are asked to determine.

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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, to find ƒ(-2), you would locate -2 on the x-axis of the graph and identify the corresponding y-value. This process is fundamental in understanding how functions behave at different points.

Graph Interpretation

Graph interpretation is the ability to read and analyze the information presented in a graph. This includes understanding the axes, identifying key points, and recognizing trends. In this context, it is essential to accurately extract function values from the graph of y = ƒ(x) for the specified inputs.

Coordinate System

A coordinate system provides a framework for locating points in a two-dimensional space using ordered pairs (x, y). The x-axis represents the input values, while the y-axis represents the output values of the function. Understanding this system is crucial for accurately determining function values from a graph.