ALGEBRA SUGGESTED HOMEWORK AND COURSE OBJECTIVES
Sec  Obj  Suggested Homework and Course Objectives for each Section 
A5  Hwk  111 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 36) 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 1.3 151 every other odd; Sec 1.5 115 and 3153 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 oddroot 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 xaxis, yaxis, 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 xaxis, yaxis, 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  175 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 yintercept 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 (centerradius) form. (Sec 1.7: Examples 1,2) 

2.1  Hwk  1, 3, 5, 9, For 13, 15, 17, 19: add g) find f(3a); 2132 all, 33,
35(omit c), 3745 odd, 46, 47, 4962 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  17 odd, 9, 11, 13, 15, 19, 25, 31, 33, 37, 39, 4149 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 GreatestInteger). (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  123 odd, 2943 odd, 59, 61, 63, 
14.  Graphing with Reflections, Compressions/Stretching, Translations a. Identify reflections about the x or yaxis; 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  19 odd, 1327 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 15)  
3.1  Hwk  17 odd, 1321 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 710) 

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 onetoone by looking at a graph or set of ordered pairs. (Sec 4.1: Example 2) b. Given the graph of a onetoone 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 1118 omit D, H, G, do 11,
12, 1517; For 1924 omit F, do 19, 2124; 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  121 every other odd, 2549 odd,
For 5360 omit D, G, H, do 53, 54, 5759; For 6166 omit E, F, do 61, 63, 65, 66; 6773 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  131 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  111 odd, 1523 odd, 3139 odd, 4553 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 49) 

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 4,69) 