Download Sections 3.1

Math 1113 Objectives
OpenStax Algebra & Trigonometry
CHAPTER 3: FUNCTIONS
Section 3.1: Functions and Function Notation
Determine whether a relation represents a function.
Use the Vertical Line Test to determine whether a given graph is that of a function.
Find the value of a function.
Determine whether a function is one-to-one.
Use the Horizontal Line Test to determine whether a given graph is that of a 1-1
function.
Identify and sketch the “Basic Toolkit Functions” (constant, identity, absolute value,
quadratic, cubic, reciprocal, reciprocal squared, square root, and cube root).
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Page 176: Section Exercises
Section 3.2: Domain and Range
Find the domain of a function defined by an equation.
Use interval notation and set-builder notation
Find the domain and range when given a graph.
Give the domain and range of the basic toolkit functions.
Graph piecewise-defined functions.
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Section 3.3: Rates of Change and Behavior of Graphs
∆y
f (b) − f (a)
=
.
∆x
b−a
Use a graph to determine where a function is increasing, decreasing, or constant.
Find the average rate of change of a function over an interval:
Use a graph to locate local/relative extrema (maxima and minima in a neighborhood ).
Use a graph to locate global/absolute extrema (maxima and minima overall ).
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Section 3.4: Compositions of Functions
Combining functions by adding, subtracting, multiplying, or dividing.
Create a new function by composition of functions: (f ◦ g)(x) = f (g(x)).
Evaluate composite functions.
Find the domain of a composite function.
Decompose a composite function into component functions.
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Page 218: Section Exercises
Section 3.5: Transformations of Functions
Graph functions using vertical and horizontal shifts.
Graph functions using reflections about the x-axis or y-axis.
Determine whether a function is even, odd, or neither from its graph.
Graph functions using vertical and horizontal stretching and compressing.
Combine transformations.
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Section 3.6: Absolute Value Functions
Graph an absolute value function.
Solve an absolute value equation or inequality.
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Section 3.7: Inverse Functions
Verify that two functions are inverses of each other.
Determine the domain and range of an inverse function.
Restrict the domain of a function so that it will be one-to-one.
Given a function, graph the inverse relation or inverse function.
Find the inverse of a function algebraically.
Evaluate an inverse function.
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Page 264: Section Exercises
p. 267: Chapter 3 Review, Vocabulary
p. 272: Chapter 3 Review Exercises (see solutions manual)
p. 277: Chapter 3 Practice Test (see solutions manual)
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