Textbook Question
In Exercises 64–66, begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. r(x) = 2√(x + 2)
Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 3, Problem 65
Use the graph of f to find each indicated function value.
f(-2)
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Identify the point on the graph where the input value (x) is -2.
Locate the vertical line corresponding to x = -2 on the x-axis.
Find the point on the curve that intersects this vertical line at x = -2.
Determine the y-coordinate of this intersection point, which represents f(-2).
Read the y-value from the graph at this point to find the function value f(-2).
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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 of function f at 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(x) from a graph, locate the input value x on the horizontal axis, then move vertically to the graph's curve. The corresponding y-coordinate on the vertical axis is the function value f(x). This skill is crucial for interpreting graphical data.
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05:10Graphs & the Rectangular Coordinate System
Coordinate Plane and Axes
The coordinate plane consists of the x-axis (horizontal) and y-axis (vertical), which intersect at the origin. Points on the plane are given as (x, y), where x is the input and y is the output. Understanding this helps in accurately reading and plotting points on a graph.
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Related Practice
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Textbook Question
In Exercises 64–66, begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. g(x) = √(x + 3)