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 11-18)
(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 39-44)
(c) Given a reflected and translated graph, be able to determine the equation of the
original graph (Section 1.5 : Problems 55-58)
(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 x-axis and the y-axis.
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
y-axis?
(f) What can we say about the reflection of the graph of an odd function over the y-axis
as compared to its reflection over the x-axis?
(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 31-38)
(c) Given a horizontally/ vertically expanded /compressed graph, be able to determine
the equation of the original graph (Section 1.5 : Problems 31-38)
(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 1-6)
(c) Given two functions know how to find their product and quotient and evaluate this
product/quotient at given points (Section 1.6 : Problems 7-12)
(d) Know how to find the domain of the sum, difference, and product of two functions
(Section 1.6 : Problems 13-16)
(e) Know how to find the domain of the quotient of two functions (Section 1.6 : Problems
13-16)
(f) Know how to graph the sum or difference of two functions, given the graphs of each
function (Section 1.6 : Problems 33-36,37-44)

• 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 19-26)
(c) Given two functions f and g be able to determine the domain of f g and g f
(Section 1.6 : Problems 19-26 *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 45-51)

• 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
49-54)
(g) Know the point-slope 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 3-8, 15-22,
23-30, 31-38, 39-44)
(k) Be able to solve “break-even problems”, “mixture problems”, “geometry problems”,
and ”rate problems” (Workbook : p.87-90)

• 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 15-20)
(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 : 21-32)
(h) Be able to find the x and y intercepts and the vertex of the graph of a quadratic
function (Section 2.2 : Problems 33-40)
(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?