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Review Sheet  Test 2
• HORIZONTAL/VERTICAL TRANSLATIONS
(a) Know the definition of horizontal/vertical translations (p.68)
(b) Know how translations effect a graph (Section 1.5 : Problems 1118)
(c) Given a translated graph, be able to determine the equation of the original
graph
(Section 1.5 : Problems 53,54)
(d) Given a function, be able to determine the equation for any translation of
the graph
of that function (for example, given f(x) = y, translate the graph of f by h
units to
the right and k units down. What is the equation of the translated graph?)
(e) To graph f(x + h) + k, replace each point (a, b) on the graph of f with the
point_____.
• REFLECTIONS
(a) Know the definition of a reflection (p.74)
(b) Know how reflections effect a graph (Section 1.5 : Problems 3944)
(c) Given a reflected and translated graph, be able to determine the equation of
the
original graph (Section 1.5 : Problems 5558)
(d) Given a function, be able to determine the equation for any reflection of
the graph of
that function (given f(x) = y, reflect the graph of f over the xaxis and the
yaxis.
What is the equation of the reflected graph?)
(e) What can we say about the reflection of the graph of an even function over
the
yaxis?
(f) What can we say about the reflection of the graph of an odd function over
the yaxis
as compared to its reflection over the xaxis?
(g) To graph f(−x), replace each point (a, b) on the graph of f with the
point_____ .
To graph −f(x), replace each point (a, b) on the graph of f with the point______
.
• HORIZONTAL/VERTICAL EXPANSIONS/COMPRESSIONS
(a) Know the definition of horizontal/vertical expansions/compressions
(p.71,72)
(b) Know how horizontal/vertical expansions/compressions effect a graph (Section
1.5 :
Problems 3138)
(c) Given a horizontally/ vertically expanded /compressed graph, be able to
determine
the equation of the original graph (Section 1.5 : Problems 3138)
(d) Given a function, be able to determine the equation for any
horizontal/vertical
expansion/compression of the graph of that function (for example, given f(x) =
y,
compress the graph of f by a factor of 1/2 horizontally . What is the equation of
the
compressed graph?)
(e) To graph Cf(Dx), where C and D are positive real numbers , replace each point
(a, b) on the graph of f with the point______ .
• SUM, DIFFERENCE, PRODUCT, AND QUOTIENT OF FUNCTIONS
(a) Know the sum, difference, product, and quotient of two functions (p.79)
(b) Given two functions know how to find their sum and difference and evaluate
this
sum/ difference at given points (Section 1.6 : Problems 16)
(c) Given two functions know how to find their product and quotient and evaluate
this
product/quotient at given points (Section 1.6 : Problems 712)
(d) Know how to find the domain of the sum, difference, and product of two
functions
(Section 1.6 : Problems 1316)
(e) Know how to find the domain of the quotient of two functions (Section 1.6 :
Problems
1316)
(f) Know how to graph the sum or difference of two functions, given the graphs
of each
function (Section 1.6 : Problems 3336,3744)
• COMPOSITION OF FUNCTIONS
(a) Know the definition of the composition of two functions (p.84)
(b) Given two functions f and g be able to determine f g and g f, and evaluate
each
function at given points (Section 1.6 : Problems 1926)
(c) Given two functions f and g be able to determine the domain of f g and g f
(Section 1.6 : Problems 1926 *try to find the domain of these)
(d) Given a function h be able to find functions f and g with f(x) ≠ x and g(x)
≠ x
such that h(x) = (f ο g)(x) (Section 1.6 : Problems
4551)
• LINEAR FUNCTIONS
(a) Be able to determine if a function is linear (p.102)
(b) Know the definition of the slope of a line (p.102)
(c) Understand what the slope tells you about the graph of the line (p.104,
Table 2.1)
(d) Given two points on a line, or the equation of a line, be able to determine
the slope
(Section 2.1 : Problems 1,2)
(e) Know the definition of parallel/perpendicular lines, and in general what the
graphs
of two parallel/perpendicular lines look like (p.112,113)
(f) Be able to determine if two lines are parallel/perpendicular (Section 2.1 :
Problems
4954)
(g) Know the pointslope form for a line, and what information about the line
you need
in order determine it (p.108)
(h) What is the relationship between the slope intercept form of a line and the
pointslope
form of a line?
(i) What is the equation of a vertical line passing through the point (a, b)?
What is the
equation of a horizontal line passing through the point (a, b)?
(j) Given two points on a line, a point on the line and its slope, or a line
parallel to
and a point, determine the equation for the line (Section 2.1 : Problems 38,
1522,
2330, 3138, 3944)
(k) Be able to solve “breakeven problems”, “mixture problems”, “geometry
problems”,
and ”rate problems” (Workbook : p.8790)
• QUADRATIC FUNCTIONS
(a) Know the definition of the vertex of the graph of a quadratic function,
and the
definition of concave up/down (p.125)
(b) How do you determine if the graph of a quadratic function is concave up or
down?
(c) Know the definition of the general form a quadratic function (p.128)
(d) Know the definition of the standard form a quadratic function (p.127)
(e) What is the relationship between the standard form and the general form?
(f) What information do you need in order to determine the standard form of a
quadratic
function? (Section 2.2 : Problems 1520)
(g) Given a quadratic function in general form, be able to put it in standard
form
 “ completing the square ” or by “cheating” [I will show you how to “cheat” on
Monday] (Section 2.2 : 2132)
(h) Be able to find the x and y intercepts and the vertex of the graph of a
quadratic
function (Section 2.2 : Problems 3340)
(i) Be able to determine if a given quadratic function has a maximum or minimum
value, and find the maximum or minimum value (Section 2.2 : Problems 41,42)
(j) At what point on the graph does the maximum/minimum value of a quadratic
function occur?
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