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Ch. 2 - Functions and Graphs
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 2 - Functions and GraphsProblem 67
Chapter 3, Problem 67

In Exercises 65–70, use the graph of f to find each indicated function value. f(4)
Graph of a sinusoidal function y = f(x) showing values between x = -5 and x = 5 on a grid.

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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.
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Function Composition

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.
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Graphs & the Rectangular Coordinate System

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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Change of Base Property
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