Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 55

Chapter 3, Problem 55

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

Verified step by step guidance

Recall that the vertical line test is used to determine if a graph represents a function. The test states that if any vertical line intersects the graph at more than one point, then the graph does not represent a function.

Look at the graph and imagine drawing vertical lines (lines parallel to the y-axis) at various x-values across the domain of the graph.

Check if any vertical line crosses the red curve more than once. If no vertical line intersects the curve at more than one point, then y is a function of x.

In this graph, observe that for every x-value, the vertical line intersects the curve at exactly one point, meaning each x-value corresponds to only one y-value.

Therefore, based on the vertical line test, this graph represents y as 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 visual method used to determine if a graph represents a function. If any vertical line drawn through the graph intersects it at more than one point, the graph does not represent a function. This test ensures that each input (x-value) has only one output (y-value).

Definition of a Function

A function is a relation where each input corresponds to exactly one output. In terms of graphs, this means for every x-value, there is only one y-value. Understanding this definition is crucial to applying the vertical line test correctly.

Interpreting Graphs on the Cartesian Plane

Graphs on the Cartesian plane plot pairs of x and y values. Being able to read and analyze these graphs helps in identifying whether the relation shown is a function. Recognizing the shape and behavior of the curve aids in applying tests like the vertical line test.

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