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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 69
Chapter 3, Problem 69

In Exercises 65–70, use the graph of f to find each indicated function value. f(-3)
Graph of a function y = f(x) showing peaks and valleys between x = -5 and x = 5 on a coordinate plane.

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Identify the point on the graph where the input value (x) is -3. This means you need to look along the x-axis at -3 and find the corresponding point on the curve.
From the point where x = -3, move vertically to the curve to find the y-coordinate of the function at that x-value. This y-coordinate is the value of f(-3).
Read the y-value from the graph at x = -3 carefully. This value represents f(-3).
Write down the function value as f(-3) = y, where y is the y-coordinate you found on the graph.
Double-check the graph to ensure the point you identified corresponds exactly to x = -3 and that you have read the y-value correctly.

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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 allows you to interpret the graph and find the value of f at a specific x-coordinate.
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Reading Values from a Graph

To find f(-3) from the graph, locate x = -3 on the horizontal axis, then find the corresponding y-value on the curve. This y-value is the function's output at x = -3. Accurate reading of coordinates is essential for interpreting function values visually.
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Graphs & the Rectangular Coordinate System

Coordinate Plane and Axes

The coordinate plane consists of the x-axis (horizontal) and y-axis (vertical). Points on the graph are given as (x, y), where x is the input and y is the output. Understanding this helps in identifying the correct point on the graph to evaluate the function.
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Related Practice
Textbook Question

Find a. (fog) (x) b. the domain of f o g. f(x) = x/(x+1), g(x) = 4/x

Textbook Question

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

Find g(-4)

Textbook Question

Graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. (x − 2)²+(y+3)² = 4, y = x - 3

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Textbook Question

Begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. g(x) = √(x+1)

Textbook Question

Find a. (fog) (x) b. the domain of f o g.

f(x) = √x, g(x) = x − 2

Textbook Question

In Exercises 67–69, begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. r(x) = (1/2) |x + 2|