Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

3. Functions

Intro to Functions & Their Graphs

College Algebra

3. Functions

Intro to Functions & Their Graphs

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1:38 minutes

Problem 65

Textbook Question

In Exercises 65–70, use the graph of f to find each indicated function value.
f(-2)

Verified step by step guidance

Locate the x-coordinate -2 on the horizontal axis.

Move vertically from x = -2 until you intersect the graph of the function f.

Identify the y-coordinate of the point where the vertical line intersects the graph.

The y-coordinate at this intersection point is the value of f(-2).

Read the y-coordinate value from the graph.

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Key Concepts

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

Function Value

The function value, denoted as f(x), represents the output of a function for a given input x. In this context, finding f(-2) means determining the y-coordinate of the graph at x = -2. This is essential for understanding how to evaluate functions graphically.

Graph Interpretation

Interpreting a graph involves analyzing the plotted points and curves to extract information about the function. This includes identifying key features such as intercepts, slopes, and specific function values at given x-coordinates, which is crucial for answering the question about f(-2).

Coordinate System

A coordinate system provides a framework for locating points in a plane using pairs of numbers (x, y). In this case, the x-axis represents the input values, while the y-axis represents the output values of the function. Understanding this system is vital for accurately reading the graph and finding the desired function value.