Ch. 2 - Functions and Graphs

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

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 67

Chapter 3, Problem 67

In Exercises 65–70, use the graph of f to find each indicated function value. f(4)

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Identify the point on the graph where the input value (x) is 4.

Locate the vertical line corresponding to x = 4 on the x-axis.

Find the point on the curve of the function f(x) that intersects this vertical line.

Determine the y-coordinate of this intersection point, which represents the value of f(4).

Read the y-value from the graph at x = 4 without calculating, just noting the position on the y-axis.

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Key Concepts

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

Function and Function Notation

A function assigns each input exactly one output. The notation f(x) represents the output value of the function f at the input x. Understanding this notation is essential to interpret and evaluate function values from graphs or equations.

Reading Values from a Graph

To find f(4) from a graph, locate the input value x = 4 on the x-axis, then find the corresponding point on the curve. The y-coordinate of this point is the function value f(4). This skill is crucial for interpreting graphical data.

Properties of Sinusoidal Functions

Sinusoidal functions, like sine and cosine, have wave-like patterns with regular peaks and troughs. Recognizing these patterns helps predict function values and understand periodic behavior, which is useful when analyzing graphs of such functions.

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