College Algebra Exam File - Fall Test #1
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1 College Algebra Exam File - Fall 010 Test #1 1.) For each of the following graphs, indicate (/) whether it is the graph of a function and if so, whether it the graph of one-to one function. Circle your answers. A B C Function one-to-one function Function one-to-one function Function one-to-one function For exercises #-4, consider the following functions. f(x) = x - 5 g(x) = h(x) =.) Find the domain of: a.) f b.) g c.) h d.) (h f)(x) 3.) Evaluate the following. a.) f(3) b.) g(-7) c.) h(1+a) d.) (h g)() e.) (f f)(0) 4.) Find the range of: a.) f b.) g 5.) Consider the function, f(x) = 4-7x. a.) Prove algebraically that f(x) is one-to-one. b.) Find f -1 (x).
2 6.) Suppose the graph of f(x) looks like this (each tick mark detes 1 unit). Graph g(x) = f(x + 1) + 3. For exercises #7-8, consider the function f(x) = x 3 + x - 9.7x ) Find the following: a.) x-intercept(s) b.) y-intercept(s) c.) local maximum d.) local minimum e.) interval(s) where increasing f.) interval(s) where decreasing 8.) Find the following: a.) domain b.) range c.) absolute maximum d.) absolute minimum e.) the graph 9.) There are three consecutive odd numbers whose product is a.) Write an equation representing the above statement. b.) Using your calculator, solve the equation to find the three numbers. 10.) Use your calculator to find the intersection(s) of the following curves. y = x - x - 7 y = x ) A farmer has 00 feet of fencing. He wants to create a rectangular pasture. a.) Write a function, A(x), that gives the area, A, as a function of the length, x. b.) Find the dimensions of the rectangle that gives the largest area he can enclose. c.) Find the largest area he can enclose. Exam # 1.) Find an equation for the line that goes through the points (5, 3) and (4, -)..) Find an equation for the line on the point (5, -) and perpendicular to the line 3x - 6y = 1. 3.) No calculator. Solve the following equation by factoring. Exact answers only. x - x - 6 = 6 4.) No calculator. Solve the following equation by the quadratic formula. 5x - x - 4 = 5.) Solve the following equation. Feel free to use your calculator. 8.3x x = 0
3 6.) Solve the following equation. You may use your calculator. x x = 0 7.) No calculator. Solve the following equation exactly. x x 1/ ) No calculator. Find the exact solution(s) for x 3 3x ) Write each of the following as complex numbers in standard form. a.) ( - 5 i) + (3 + i) b.) ( - 5 i) - (3 + i) c.) ( - 5 i)(3 + i) d.) 5i 3 i e.) i ) Find an equation for the parabola that has a vertex of (5, -) and goes through (1, 7). 11.) Consider the following table of values. x y a.) Draw a scatter plot of the data. b.) Write the quadratic function that best fits the data. c.) Draw the function from b.) on your scatter plot from a.). d.) Does the function fit the data well? Why? 1.) Find four consecutive odd numbers who sum is 616. Be sure to show the equation you use to solve the problem. 13.) The diagonal of a rectangle is 1 inches. The area is 50 square inches. Find the dimensions of the rectangle. 14.) Let f(x) = x + 1x - 5. Find the vertex and all intercepts. Graph the function. Exam #3 1/ 1.) No calculator. Solve the following equation exactly. x x 3 0.) No calculator. Find the exact solution(s) for x 3 3x ) Solve the inequality. 5-3x > 7 4.) Solve the following inequality. Give your answer in graph form. 3x - < 11 5.) Consider the following table of values. x y a.) Draw a scatter plot of the data. b.) Write the logarithmic function that best fits the data. c.) Draw the function from b.) on your scatter plot from a.). d.) Does the function fit the data well? Why? 6.) Solve the given equation exactly. No calculator. All work must be shown. 4 x-3 = 8 5x+1 7.) Graph the following function. Find all of the following.
4 3x 3x 36 f ( x) x 4 x-intercept(s), y-intercept(s), horizontal asymptote(s),vertical asymptote(s), local minima, local maxima, domain, range, intervals where increasing, intervals where decreasing, GRAPH 8.) Solve the equation using your calculator. 5 x-4 = 70 9.) Suppose you invest $8000 at an interest rate of 3.5%. Find the balance after 5 years if the interest is compounded quarterly. Be sure to write down the formula you are using. 10.) Suppose y varies directly as x. If y = 3, when x = 9, find y when x = ) The half-life of Actinium-8 is 6.13 hours. If 10 grams are present w, how much will be present in 3 days? 1.) Without using your calculator, solve following the equation. log log 3 x = 13.) Use your calculator to solve the following equation. log 3 x + log 5 x = Exam #4 1.) Solve the following system of equations without your calculator. Use the method of substitution. x y = 7 x + y = 4.) Solve the following system of equations without your calculator. Use the matrix method of elimination. x y = 7 x + y = 4 3.) Solve the following system of equations. Use your calculator and any method involving matrices. EXPLAIN HOW YOU USED YOUR CALCULATOR x 1.57y = x + y = 4 4.) Graph the solution to the following system of inequalities. x + y < 5 3x + y > 1 5.) Find the maximum and minimum values of the function and the points at which they occur, subject to the given constraints. z = x + 5y 4x + y < 1 x + y < 6 x > 0 y > 0 6.) Given an arithmetic sequence with a 1 = and a 3 = 8, find the following without using your calculator. a.) a b.) a 15 c.) S 15 7.) Consider the geometric sequence whose first two terms are a 1 = 1 and a = -6. a.) Find the 3-rd term. b.) Find the sum of the first 3 terms. (you may use your calculator) c.) Find the sum of the infinite series if it exists. If it does t exist, tell why.
5 8.) The menu at a restaurant has 1 appetizers, five salads, four soups, 36 entrees, 1 drinks and eight desserts. How many different meals can you order if you order one of each item? 9.) You roll two standard six-sided dice and add the numbers. Find the probability of getting a sum less than ) Use your calculator to evaluate the following sum. 11.) Without your calculator, evaluate the following sum. 1.) You are making license plates with three letters followed by three numbers. If letters may t be repeated, how many license plates are possible? Final Exam 1.) Find the domain and range of the function..) Use the given conditions to write an equation for the line. Passing through (-5,1) and (-8, -5) 3.) The table shows the time spent researching the stock market each week and the percent gain for an investor. Research (hours) Gain % a.) Determine the linear function that best fits the data (round to two decimal places). b.) Tell whether the line fits the data well, based on the correlation coefficient. 4.) For functions, and, perform the indicated operation and simplify. 5.) Solve the following quadratic equation using the Quadratic Formula. 6.) Using the compound interest formula, find the accumulated value of an investment if $5,000 is compounded monthly at 11% for 5 years. 7.) Solve the logarithmic equation. Be sure to show all your work, do t use a calculator. 8.) Solve the following system of equation by the elimination or substitution method. Be sure to show all work, do t use a calculator. 9.) Suppose f(x) = 3x + and g(x) = x - 1.
6 a.) Find (f - g)(3). b.) Find (g g)(). c.) Find f -1 (x) if it exists. If it does t exist, explain why. d.) Find g -1 (x) if it exists. If it does t exist, explain why. 10.) Consider the arithmetic sequence with a 1 = 4 and a 3 = 8 (pay CLOSE attention to the subscripts). Find the following: a.) a 85 b.) S ) Without using your calculator, solve the equation exactly. 3x 1 4x 0 1.) Solve the following inequality. 7-5x < ) Solve the following inequality. x - 4x - 5 > ) Solve the following equation. 3x - = ) Use your calculator to solve the following equation. e x 3 4log x 16.) Suppose the graph in the left hand grid is f(x). On the right hand grid, graph g(x) = f(x+3) ) Graph the following function. Fill in all of the following. x x 6 f ( x) 3x 3 x-intercept(s) y-intercept(s) horizontal asymptote(s) vertical asymptote(s) local minima GRAPH 18.) Solve the following equation by hand. Exact Answer Only!!! 7-3x = 81 x-1 19.) You roll two standard six-sided dice and add the numbers. Find the probability of getting a sum less than 6. 0.) Using your calculator, solve the equation log 7 (x +1) - log 5 x - 1 = 0. 1.) Solve the following system of equations. Use your calculator. 4.55x y = x - e y = 4.75.) The menu at a restaurant has 1 appetizers, five salads, four soups, 36 entrees, 1 drinks and eight desserts. How many different meals can you order if you order one of each item? 3.) Solve the following equation by factoring. No calculator. x - 5x - 6 = 8 4.) Solve the given equation exactly. log x + log (x - 4) = ( calculator) 5.) Solve the given equation exactly. x + x 1/ - 8 = 0 ( calculator)
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