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ALGEBRA SUGGESTED HOMEWORK AND COURSE OBJECTIVES

Sec Obj Suggested Homework and Course Objectives for each Section
A5 Hwk 1-11 odd
  1. Rational Expressions
a. Equivalent Rational Expressions. (Class Examples)
b. Multiply or divide rational expressions; simplify. (Sec A5: Example 2)
c. Add or subtract rational expressions; simplify. (Sec A5: Examples 3-6)
d. Simplify mixed quotient. (Sec A5: Example 7)
A6 Hwk 37, 39, 41, 43, 47, 57, 61, 63, 65
  2. Understand the meaning of rational exponents; simplify numbers raised to rational exponents. (Sec A6:
Example 7)
  3. Special Factoring Techniques
a. Factor by grouping. (refer to your class notes; may also refer to Sec A3: Example 3f)
b. Factor and simplify an expression containing rational exponents. (Sec A6: Example 10)
c. Factor and simplify an expression containing rational exponents and a common binomial factor. (Class
Examples)
CN Hwk Sec 1.3 1-51 every other odd; Sec 1.5 1-15 and 31-53 every other odd
  4. Solving Equations
a. Solve linear equations. (Refer to your class notes; may also refer to Sec A1: Examples 12)
b. Solve quadratic equations (including Quadratic Formula). (Refer to your class notes; may also refer to
Sec 1.3: Algebraic solution of Example 6; Sec A2: Example 3)
c. Solve rational equations. (Class Examples)
d. Solve higher order equations. Understand the existence of real number roots. (refer to your class notes;
may also refer to Sec A1: Example 13a)
e. Solve equations that contain even- or odd-root radicals. (Refer to your class notes; may also refer to Sec
1.3: Algebraic Solutions of Example 10)
  5. Inequalities
a. Solve linear inequality. and express the solution in interval notation. (Refer to your class notes; may
also refer to Sec.1.5: Examples 7, 8)
b. Express the solution to inequalities in interval notation. (Refer to your class notes; may also refer to
Sec.1.5: Example 1)
c. Express the solution to inequalities in interval notation and understanding the terms “or” and “and”.
(Refer to your class notes.)
1.1 Hwk 1, 21, 23, 31, 33, 49, 55, 57
  6. Rectangular Coordinate System
a. Understand plotting points on the Rectangular Coordinate Sytem. (Sec 1.1: Figure 2, 3)
b. Recall and use the distance formula. (Sec 1.1: Example 2)
c. Recall and use the midpoint formula. (Sec 1.1: Example 5)
1.2 Hwk Recall and use the midpoint formula. (Sec 1.1: Example 5)
1.2 Hwk 3, 7, 9; For 11, 19, 25, 27: sketch the graph by hand by making a table of values, find any
intercepts; 31, 33, 37, 41, 47, 49, 51, 53, 54, 57, 59, 61, 63; For 65, 67, 69, 71, 73: find the
intercepts, test for symmetry, you do not need to graph.
  7. General Graphing Principles
a. Understand what it means for a point (a,b) to be on the graph of an equation. (Sec 1.2: Example
1,2,9,10)
b. Identify intercepts from a graph or from an equation. (Sec 1.2: Example 4,5)
c. Symmetry
Determine symmetry with respect to the x-axis, y-axis, or origin from a graph (Sec 1.2: Figure 27)
Given a point on a graph, give the coordinates of a point that must also be on the graph if the graph is
symmetric with respect to the x-axis, y-axis, or origin. (Sec 1.2: Example 7)
Algebraically determine if the graph of an equation has any symmetry. (Sec 1.2: Example 8)
1.6 Hwk 1-75 odd, 85, 87, 89
  8. Linear Equations
a. Calculate and interpret slope. (Sec 1.6: Example 1)
b. Graph lines by hand by obtaining the x- and y- intercepts or any two points. (Sec 1.6: Example 2, 3)
c. Identify the slope and y-intercept from the equation of a line. (Sec 1.6: Example 7)
d. Write the equation of a horizontal or vertical line. (Sec 1.6: Example 3, 5)
Write the equation of a line given two points on the line or given a point and the slope. (Sec 1.6: Ex. 4)
e. Write the equation for a linear relationship described in an applications problem. (Class Examples)
f. Write the equation of a line that goes through a given point that is parallel or perpendicular to a given
line. (Sec 1.6: Example 9, 10, 11)
1.7 Hwk For 5, 7, 9, 11: Just write the standard form; 15, 17 (You will not be asked to complete the
square and obtain the general form of the equation of a circle.)
  9. Identify the center and radius and graph a circle when given the equation in standard (center-radius)
form. (Sec 1.7: Examples 1,2)
2.1 Hwk 1, 3, 5, 9, For 13, 15, 17, 19: add g) find f(3a); 21-32 all, 33, 35(omit c), 37-45 odd, 46, 47, 49-62
all, 67, 69
  10. Functions
a. Identify the graph of a function; determine whether a relation represents a function. (Sec 2.1: Examples
1,2,7)
b. Find value of a function. (Sec 2.1: Example 4)
c. Find the domain and range of a function from a graph. (Sec 2.1: Example 8)
Find the domain of a function from the equation of the function. (Sec 2.1: Example 6)
d. Obtain information from and about the graph of a function. (Sec 2.1: Examples 8,9)
2.3 Hwk 1-7 odd, 9, 11, 13, 15, 19, 25, 31, 33, 37, 39, 41-49 odd, 55, 63, 65, 71
  11. Properties of Functions
a. From a graph, identify intervals where a function is increasing, decreasing, or constant. (Sec 2.3:
Example 3)
b. From a graph, identify local maximums or local minimums and where they occur. (Sec 2.3: Figure 24)
c. Find the average rate of change of a function. (Sec 2.3: Example 2)
d. Find the slope of the secant line containing (x, f(x)) and (x + h, f(x + h)) on the graph of a function y =
f(x). (Sec 2.3)
e. Determine, from a graph or from an equation, whether a function is even or odd. (Sec 2.3: Example 5,6)
  12. Recognize the graph, equation, and properties, of any of the basic functions in the Library of Functions
(except Greatest-Integer). (Sec 2.3)
  13. Functions defined Piecewise
a. Evaluate a function defined piecewise. (Sec 2.3: Example 7)
b. Graph a function defined piecewise. (Sec 2.3: Example 7)
2.4 Hwk 1-23 odd, 29-43 odd, 59, 61, 63,
  14. Graphing with Reflections, Compressions/Stretching, Translations
a. Identify reflections about the x- or y-axis; graph a function reflected about either axis. Understand the
affect of a reflection about a coordinate axis on the coordinates of a point on a graph or on the domain or
range of the function. (Sec 2.4: Figure 46)
b. Identify compressing or stretching factors from an equation; graph a function with these. Understand the
affect of a compressing or stretching factor on the coordinates of a point on a graph or on the domain or
range of the function. (Sec 2.4: Example 3)
c. Identify vertical or horizontal translations from an equation; graph a function with these. (Sec 2.4:
Example 1,2)
2.5 Hwk 1-9 odd, 13-27 odd, 31, 33, 37, 47, 49, 51
  15. Form the sum, difference, product, or quotient of two functions; evaluate; give the domain of the new
function. (Sec 2.5: Example 1)
  16. Function Composition
a. Form the composite of two functions; evaluate a composite function. (Sec 2.5: Examples 2, 4)
b. Find the domain of a composite function. (Sec 2.5: Example 3)
2.6 Hwk 1a, 3a
  17. Construct and analyze functions and math models. (Sec 2.6: Examples 1-5)
3.1 Hwk 1-7 odd, 13-21 odd, 25, 29, 35, 37, 39, 41, 43, 43, 49, 53, 57, 59, 61, 63, 65, 67, 71, 73, 75 abc
  18. Quadratic Functions
a. Given a quadratic function in the form y = ax^2 +bx + c, find the vertex, all intercepts, and sketch the
graph by hand. (Sec 3.1: Examples 1 – 5)
b. Given a quadratic function in the form y = a(x – h)^2 + k, find the vertex, all intercepts, and sketch the
graph by hand. (Apply graphing translations from Sec 2.4)
c. Obtain the quadratic function needed to solve an applications problem; find the maximum or minimum
value of a quadratic function. (Sec 3.1: Example 7-10)
3.2 Hwk Figure 19 and 20
  19. Power Functions
a. Graph a power function by hand; give domain and range and identify intervals where increasing or
decreasing. (Sec 3.2: Figure 19, 20)
3.8 Hwk Solve algebraically. 1, 3, 9, 11 17, 25, 27, 33, 39, 41, 45, 47, 49, 53
  20. Polynomial and Rational Inequalities
a. Solve a polynomial inequality algebraically. (Sec 3.8: Example 1, 2)
b. Solve a rational inequality algebraically. (Sec 3.8: Example 3)
c. Given a rational inequality, find the number of partitioning values needed to solve. (Class Examples.)
4.1 Hwk 1, 3, 5, 9, 11, 15, 17, 19; For 21, 25, 27: verify and graph.; For 29: just verify; 33, 35, 37, 39, 41;
For 47, 49, 53: just find the inverse
  21. Inverse Functions
a. Determine whether a function is one-to-one by looking at a graph or set of ordered pairs. (Sec 4.1:
Example 2)
b. Given the graph of a one-to-one function, draw the graph of the inverse function. (Sec 4.1: Example 4)
c. Use composition to determine if two functions are inverses. (Sec 4.1: Example 6)
d. Given an equation of a function, find an equation of the inverse function, f-1. (Sec 4.1: Example 6, 7)
4.2 Hwk For 11-18 omit D, H, G, do 11, 12, 15-17; For 19-24 omit F, do 19, 21-24; 25, 27, 37, 39, 41; and
4.5: 19,31
  22. Exponential Functions
a. Given an exponential function, give the domain, range, intervals where increasing or decreasing, find
intercepts when possible, sketch the graph by hand. (Sec 4.2: Example 2, 3)
b. Given an exponential function with a translation, give the domain, range, intervals where increasing or
decreasing, find intercepts when possible, sketch the graph by hand. (Sec 4.2: Example 4,5)
c. Use a calculator to evaluate exponential expressions, including applications problems. (Sec 4.2:
Example 1)
d. Solve exponential equations by obtaining the same base. (Sec 4.5, Example 4)
4.3 Hwk 1-21 every other odd, 25-49 odd, For 53-60 omit D, G, H, do 53, 54, 57-59;
For 61-66 omit E, F, do 61, 63, 65, 66; 67-73 odd,
  23. Logarithmic Functions
a. Evaluate logarithmic functions exactly. Identify when logarithmic functions are defined and when not
defined. (Sec 4.3: Example 4)
b. Given a logarithmic function, give the domain, range, intervals where increasing or decreasing, find
intercepts when possible, sketch the graph by hand. (Sec 4.3: Figure 25)
c. Given a logarithmic function with a translation, give the domain, range, intervals where increasing or
decreasing, find intercepts when possible, sketch the graph by hand. (Sec 4.3: Example 6, 7)
d. Find the domain of a logarithmic function. (Sec 4.3: Example 5)
4.4 Hwk 1-31 odd, 35,41
  24. Properties of Logarithms
a. Understand when and how to apply basic logarithm properties. (Sec 4.4: Examples 1,2)
b. Understand the inverse function relationship between exponential and logarithmic functions. Simplify
expressions using this relationship. (Sec 4.4: Example 2)
c. Write a logarithmic expression as a sum or difference of logarithms. (Sec 4.4: Example 3, 4, 5) Write a
logarithmic expression as a single logarithm. (Sec 4.4: Example 6)
4.5 Hwk 1-11 odd, 15-23 odd, 31-39 odd, 45-53 odd
  25. Solve Exponential Equations
a. Solve exponential equations algebraically. (Sec 4.5: Example 7,8,9)
b. Solve exponential equations algebraically when base is e or 10. (Class Examples)
  26. Solve Logarithmic Equations
a. Solve logarithmic equations algebraically. (Sec 4.5: Example 2)
b. Solve logarithmic equations algebraically using the definition of logarithms. (Sec 4.5: Example 1, 3)
  27. Solve other kinds of equations involving exponential functions. (Class Examples)
  28. Solve other kinds of equations involving logarithmic functions. (Class Examples)
4.6 Hwk 1, 13, 29, 31, 33, 37
  29. Compound Interest
a. Future Value or Present Value with quarterly or monthly compounding. (Sec 4.6: Examples 1,3, 4, 5)
b. Future Value or Present Value with continuous compounding. (Sec 4.6: Examples 3, 4, 5)
c. Determine time required to double or triple an amount of money. (Sec 4.6: Example 7)
10.1 Hwk 3, 11, 15, 17, 21, 25
  30. Solve, algebraically, 2 linear equations in 2 unknowns; interpret the solution graphically. (Sec 10.1:
Example 4-9)
10.7 Hwk 1, 5, 11
  31. Solve, algebraically, a system of nonlinear equations in two unknowns. (Sec 10.7: Examples 1,2)
10.8 Hwk 1, 3, 9, 11, 13, 21, 23
  32. Linear Inequalities
a. Graph a linear inequality. (Sec 10.8: Examples 1, 3)
b. Graph a system of linear inequalities. (Sec 10.8: Examples 4,6-9)