# 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?

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