Math 155 (DoVan) Exam 1 Review (Sections 3.1, 3.2, 5.1, 5.2, Chapters 2 & 4)

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1 Chapter 2: Functions and Linear Functions 1. Know the definition of a relation. Math 155 (DoVan) Exam 1 Review (Sections 3.1, 3.2, 5.1, 5.2, Chapters 2 & 4) 2. Know the definition of a function. 3. What is the domain and range of a relation/function? 4. How does the vertical line test show whether a graph represents a function or not? 5. How do you read the equation: y = f(x)? 6. What does y = f(x) translate into words? 7. Given functions f(x) and g(x), state the formula for the following algebra of functions. a) The sum of two functions: b) The difference of two functions: c) The product of two functions: d) The quotient of two functions: Example 1. Given the set of ordered pairs: {(-3, 0), (-2, 6), (2, 0), (-5, 3)} a) State the domain of the set. b) State the range of the set. c) Is this set a function? Explain your answer. 1

2 Example 2. Given the functions f(x) = x 2 x, and g(x) = 3 2x Find and simplify the following. a) (f g)(x) b) (f )(2a) b) (fg)(-1) 8. How do you find the x-intercept of a line? The y-intercept? 9. What is the formula for the slope of a line? 10. What is the standard form of a linear equation in two variables? 11. What is the point-slope form of a line? 12. What is the slope-intercept form of a line? 13. What is the relationship of the slope of two parallel lines? 14. What is the relationship of the slope of two Perpendicular lines? Example 3. Find the equation of the line that contains points (3, -2) and (5, 1) in slope-intercept form. Example 4. The equation of Line A is 2x 3y = 5. Line B contains the point (3, -1) and is perpendicular to Line A. Find the equation of Line B in STANDARD form without fractions or decimals. 2

3 Sections 3.1 & 3.2: Systems of Linear Equations 1. What does it mean to be the solution to a system of linear equations? 2. What methods are used to find the solution to a system of linear equations? 3. What are the possible cases for the solution to a system of linear equations? 4. What is the solution set for a system of linear equations with the same slope (parallel lines)? 5. What is the Revenue Function? 6. What is the Cost Function? 7. What is the Profit Function? 8. What is the simple interest formula? (Optional) Example 1. Solve the system of linear equations using either the substitution or addition method. a) 3x 7y = 1 2x 3y = -1 b) 6x 2y = 4 3x y = 4 Chapter 4: Inequalities and Problem solving 1. What must you do in an inequality when you multiply or divide by a negative number? 2. What does Intersection mean for two sets? 3. What does Union mean for two sets? 3

4 4. When graphing a solution set on the number line, when do you use parentheses? When do you use Square brackets? 5. How do you solve a compound inequality? 6. What do you do when solving a compound inequality with the connective word and? With the connective word or? Example 1. Solve the compound inequality. Write the solution set using interval notation and graphed on the number line. a) 3x 5 > -2 AND 7 x > 2 b) 4(x 3) > 2x 9 OR x 6 < How do you solve an absolute-value equation? Example 2. Solve the absolute-value equation. 2x + 5 = 6 x 8. When solving absolute-value inequalities, what do you do to remove the absolute value symbols if a) the problem contains < or <? b) the problem contains > or >? 4

5 Example 3. Solve the absolute value inequalities. Write the solution set using interval notation and graphed on the number line. a) x < 16 b) 4 3x < 2 Inequalities in Two Variables (4.4) 9. What is the solution set to a linear inequality in two variables? 10. What is the procedure for graphing a linear inequality in two variables? 11. When is a dotted line used to graph a linear inequality on the rectangular plane? When is a solid line used? 12. What is the solution set to a System of Linear Inequalities? Example 4: Solve the system. Be clear with your solution set. y > 3x 1 2x + y < 2 y 3 < 0 5

6 Sections 5.1 & 5.2: Polynomials, Polynomial Functions 1. Know your Polynomial Vocabulary: a) Monomial b) Binomial c) Trinomial d) Degree of a term e) Degree of a polynomial f) Standard form of a polynomial g) Coefficient h) Leading Coefficient i) Constant term 2. Know the End behavior of a polynomial graph. For the generic polynomial function y = ax n determine the end behavior when: n is even n is odd a > 0 a < 0 3. How do you Add or Subtract Polynomials? 6

7 4. State the rules of exponents. a) b) c) d) e) f) g) 5. How do you Multiply Polynomials? 6. What does FOIL represent? 7. When can you use FOIL? 8. What are the Special Products? a) b) c) Textbook Review: 1. Read Chapter 2 Summary on pages Read Chapter 3 Summary on pages Read Chapter 4 Summary on pages , omit section Read Chapter 5 Summary on pages for section 5.1 & 5.2 only. 7