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

2. Graphs of Equations

Graphs and Coordinates

College Algebra

2. Graphs of Equations

Graphs and Coordinates

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0:46 minutes

Problem 15

Textbook Question

Use the vertical line test to identify graphs in which y is a function of x.

Verified step by step guidance

Step 1: Understand the vertical line test. The vertical line test is a method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function.

Step 2: Observe the graph provided. The graph shows a blue curve plotted on a coordinate plane. The curve appears to loop and cross itself in certain areas.

Step 3: Apply the vertical line test. Imagine drawing vertical lines across the graph at various x-values. Check if any vertical line intersects the graph at more than one point.

Step 4: Identify intersections. In the provided graph, there are regions where a vertical line would intersect the curve at multiple points. For example, near the loop in the graph, a vertical line would cross the curve at more than one location.

Step 5: Conclude based on the test. Since there are vertical lines that intersect the graph at more than one point, the graph does not represent a function of x.

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Key Concepts

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

Vertical Line Test

The vertical line test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function, as a function can only have one output (y-value) for each input (x-value). This test is essential for identifying functions visually.

Functions

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output. In mathematical terms, a function f can be expressed as f(x) = y, where x is the input and y is the output. Understanding the definition of functions is crucial for applying the vertical line test effectively.

Graph Interpretation

Graph interpretation involves analyzing the visual representation of data or mathematical relationships. It requires understanding the axes, scales, and shapes of graphs to draw conclusions about the relationships they depict. This skill is vital for applying the vertical line test and determining whether a graph represents a function.