Math 242 EXAM 1 STUDY GUIDE
DEFINITIONS AND VOCABULARY:
Solutions or roots of an equation (p145)
Graph of an equation (p14)
Intercepts (p17)
Symmetry: x-axis, y-axis, origin (p18)
Circle, center and radius (p20)
Function, domain and range (p40)
Piecewise-defined function (p43)
Implied domain (p44)
Graph of a function (p54)
Vertical line test (p55)
Zero of a function (p56)
Increasing, decreasing, and constant
functions (p57)
Relative maximum and minimum (p58)
Even and odd functions (p60)
Sequence, terms (p642)
Recursive definition for a sequence (p644)
Factorial (p644)
Parent function graphs (p70)
Shift (p74))
Reflection (p76)
Stretch/compression (p78)
Sum, difference, product, and quotient functions
(p84)
Function composition (p86)
FORMULAS:
Standard form for a circle (p20): 222
()()
x
hykr−+−=
Difference quotient (p46): ()()
f
xh fx
h
+−
Average rate of change (p59): 21
21
() ()
f
xfx
xx
−
−
YOU SHOULD BE ABLE TO:
Solve linear, quadratic, rational, radical and absolute value equations algebraically and graphically
Solve linear and absolute value inequalities algebraically and graphically and graph the solution set
Find the x-intercepts and y-intercepts for a graph or function
Test an equation for symmetry
Use symmetry to graph equations
Graph a circle
Write the equation of a circle satisfying certain conditions
Evaluate a function by hand, from a graph or table, and using your calculator
Find the domain and range of a function from the equation or the graph
Identify a function algebraically or graphically
Evaluate and graph piecewise-defined functions
Find zeros of a function algebraically and graphically
Find relative maximum or minimum values of a function from a graph
Use your calculator to approximate local extrema (minimum and maximum points)
Find and simplify a difference quotient
Find the average rate of change for a function between two points
Determine the intervals for which a function is increasing, decreasing, or constant
Determine whether a function is odd, even, or neither algebraically and graphically
Find the terms of a sequence defined as a function or defined recursively by hand and using your calculator
Graph the terms of a sequence
Find the formula for the nth term of a sequence
Evaluate a factorial
Simplify factorial expressions
Interpret an equation in terms of transformations of a basic function
Graph transformations of a function
Find the sum, difference, product and quotient functions (using equations, tables, or graphs) and their domains
Find the composition of two functions (using equations, tables, or graphs) and its domain
Find two functions f and g whose composition is a given function h
REVIEW PROBLEMS:
Review Exercises (p117): 25-44, 67-77, 79-138; (p715): 1-12
Chapter Test (p123): 3-6, 10-19; (p719): 1, 2