FINAL EXAM SECTIONS AND OBJECTIVES FOR COLLEGE ALGEBRA

Transcription

1 FINAL EXAM SECTIONS AND OBJECTIVES FOR COLLEGE ALGEBRA 1.1 Solve linear equations and equations that lead to linear equations. a) Solve the equation: 1 (x + 5) 4 = 1 (2x 1) 2 3 b) Solve the equation: 3x + 2 = 3 x 1 x Solve quadratic equations by factoring, the square root property, and the quadratic formula. a) Solve the equation: 2x 2 = x + 3 b) Solve the equation: (x 2) 2 = 16 c) Solve the equation: x 2 4x + 2 = Solve radical equations. a) Solve the equation: 3x + 4 = 2 b) Solve the equation: 15 2x = x 1.5 Solve linear inequalities and combined inequalities. a) Solve the inequality and write the solution set in interval notation: 8 4(2 x) 2x b) Solve the inequality and write the solution set in interval notation: 5 < 3x 2 < Solve absolute value equations and absolute value inequalities. a) Solve the equation: 2x = 7 b) Solve the inequality, write the solution set in interval notation and graph the solution set: 2x c) Solve the inequality, write the solution set in interval notation and graph the solution set: 2x 5 > Determine the slope of a line, the equation of a line, the intercepts, and the graph of a line. a) Find the slope of the line containing the points (1, 2) and (5, -3). b) Draw the graph of the line containing the point (3, 2) and has a slope of m = 3 4. c) Find the equation of the line with slope 4 that contains the point (1, 2) in slope intercept form. d) Find the equation of the horizontal line containing the point (3, 2). e) Find the equation of the line containing the two points (2, 3) and (-4, 5) in slope intercept form. f) Graph the equation 2x + 4y = 8 by finding its intercepts. g) Find the slope and y-intercept of the equation 2x + 4y = Determine if a relation represents a function, evaluate functions, and find the domain of functions. a) Determine whether the relation is a function: { (-3, 9), (-2, 4), (0, 0), (1, 1), (-3, 8)} b) Given f(x) = 2x 2 3x, evaluate f(3), f( -x), f(x+3). c) Find the domain of f(x) = x 2 + 5x

2 d) Find the domain of f(x) = 3x x 2 4 e) Find the domain of f(x) = 4 3x 3.2 Determine if a given graph represents a function, and obtain information given the graph or equation of a function including the domain, range, intercepts, and symmetry. a) Determine if the graph is the graph of a function. b) Determine if the graph is the graph of a function. c) Use the given graph of the function f to answer parts (a)-(n).

3 d) Answer the questions about the given function. 3.3 Use a graph to obtain information about a function such as intercepts, domain and range, intervals where the function is increasing, decreasing, or constant, and whether the function is even, odd, or neither. 3.4 Evaluate piecewise-defined functions. 2x + 1, 3 x < 1 Given f(x) = { 2, x = 1, find f(-2), f(1), f(2). x 2, x > Solve linear applications involving cost functions, revenue functions, or supply and demand functions. a)

4 b) 4.3 Determine if the quadratic function has a maximum or minimum value and find the maximum or minimum function value. a) Determine whether the quadratic function f(x) = x 2 4x 5 has a maximum or a minimum value. b) Then find the maximum or minimum value. 4.5 Solve quadratic inequalities. a) Solve the inequality and write the solution set in interval notation: 2x 2 < x + 10 b) Solve the inequality and write the solution set in interval notation: x 2 + 8x > Evaluate composite functions, form composite functions and determine their domains. a) Given f(x) = 2x 2 3 and g(x) = 4x, find (f g)(1) and (g f)(1) b) Given f(x) = x 2 + 3x 1 and g(x) = 2x + 3, find (f g)(x) and state the domain of the composite function. c) Given f(x) = 1 4 and g(x) =, find (f g)(x) and state the domain of the composite x+2 x 1 function. 6.2 Determine if a function is one-to-one, find the inverse of a one-to-one function, the domains and ranges of both functions, and the graphs. a) Determine if the following function is one-to-one. b) Find the inverse of f(x) = 2x + 3. Graph f, f 1, and y = x on the same coordinate axes. State the domain and range of f and f 1. c) Find the inverse of f(x) = 2 3+x. State the domain and range of f and f Evaluate exponentials with a calculator, and solve exponential equations using like bases. a) Evaluate b) Solve the equation: 3 x+1 = 81 c) Solve the equation: 8 x+14 = 16 2

5 6.4 Change exponential statements to logarithmic statements and vice versa, evaluate logarithmic expressions, and solve logarithmic equations. a) Change the exponential statement to an equivalent statement involving a logarithm. a 4 = 24 b) Change the logarithmic statement to an equivalent statement involving an exponent. log 3 5 = c c) Evaluate log d) Solve the equation: log 3 (4x 7) = 2 e) Solve the equation: log x 64 = Solve exponential equations and logarithmic equations, making use of properties of logarithms where needed. a) Solve the equation: 2log 5 x = log 5 9 b) Solve the equation: log 5 (x + 6) + log 5 (x + 2) = 1 c) Solve the equation: ln x = ln(x + 6) ln(x 4) d) Solve the equation: 2 x = Solve systems of equations. 2x + y = 1 a) Solve: { 4x + 6y = 42 2x + y = 5 b) Solve: { 4x + 2y = 8 NOTE: 1. These problems are samples of these objectives. You should refer to your homework sections in MyMathLab for additional practice. 2. The solutions to these problems can be found on the MEW page at math.nicholls.edu/mew. Spring 2016 Exam Schedule for Math 100/101 Thursday, May 10:30 AM: 5TW Friday, May 8:00 AM: 3TM, 3M Tuesday, May 8:00 AM: 2TM, 2M, 1:00 PM: 4TM, 4M, 4M1 Wednesday, May 10:30 AM: 1TM, 1M, 1M1