Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problema 76

Capitolo 3, Problema 76

Use the graph of g to solve Exercises 71–76.

For what value of x is g(x) = -1?

Guida verificata passo dopo passo

Identify the value of \(y\) for which you want to find the corresponding \(x\) value. Here, we want to find \(x\) such that \(g(x) = -1\).

Look at the graph and locate the horizontal line where \(y = -1\) on the vertical axis.

Find the points on the graph where the function \(g(x)\) intersects the line \(y = -1\). These points represent the \(x\) values where \(g(x) = -1\).

Read the \(x\)-coordinate(s) of the intersection point(s) from the graph. This \(x\)-coordinate is the solution to \(g(x) = -1\).

If there are multiple intersection points, list all corresponding \(x\) values as solutions.

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Function and Function Notation

A function relates each input (x) to exactly one output (y or f(x)). Function notation, like f(x), represents the output value corresponding to the input x. Understanding this helps interpret graphs and solve for specific function values.

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Function Composition

Reading a Graph to Find Function Values

To find where a function equals a certain value, locate the y-value on the vertical axis and identify the corresponding x-values on the graph. Points where the graph crosses or touches the horizontal line y = desired value give the solution.

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Finding the Domain and Range of a Graph

Interpreting Points and Coordinates on a Graph

Each point on a graph is an ordered pair (x, y) showing input and output values. Recognizing these points allows you to determine exact values of the function at specific inputs, which is essential for solving equations like f(x) = -1.

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Graphs and Coordinates - Example

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Use the graph of g to solve Exercises 71–76.