1.) Suppose the graph of f(x) looks like this (each tick mark denotes 1 unit). x y

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1 College Algebra Summer 2014 Exam File Exam #1 1.) Suppose the graph of f(x) looks like this (each tick mark denotes 1 unit). Graph g(x) = -0.5 f(x + 1) ) Consider the following table of values. x y d.) Draw a scatter plot of the data. Write the linear function that best fits the data. Draw the function from on your scatter plot from. Tell whether the line fits the data well, based on the correlation coefficient. 3.) Find an equation for the line that goes through the points (5, 3) and (4, -2). 4.) Find an equation for the line on the point (5, -2) and perpendicular to the line 3x - 6y = 1. 5.) Solve the inequalities. Give the answer to in interval form and the one to in inequality form x < 7 3 < 2-3x < 11 6.) Suppose y varies directly as x. If y = 3, when x = 9, find y when x = 4. 7.) A company finds it can produce 25 heaters for $5950, while producing 35 heaters costs $8250. Express the cost, y, as a linear function of the number of heaters, x.

2 8.) Find an equation of the line through the point (2, 1) that is parallel to the line y - 5x = 3. 9.) Suppose the graph of f(x) looks like this (each tick mark denotes 1 unit). Graph g(x) = f(x) on the second grid. 10.) Solve for x without using your calculator. Show all work. 2x - 5 = 11 2(3x + 6) - 4 = 4(2x + 7) Exam #2 For exercises #1-3, consider the following functions. f(x) = x 2-5 g(x) = h(x) = 1.) Find the domain of: f g h d.) (h f)(x) 2.) Evaluate the following. f(3) g(-7) h(1+a) d.) (h g)(2) e.) (f f)(0) 3.) Find the range of: f g 4.) Solve the following equation. x 2 - x - 21 = 9 5.) Consider the following table of values.

3 x y d.) Draw a scatter plot of the data. Write the quadratic function that best fits the data. Draw the function from on your scatter plot from. Tell whether the function fits the data well. 6.) No calculator. Solve the following equation by factoring. Exact answers only. x 2 - x - 20 = 10 7.) No calculator. Solve the following equation by the quadratic formula. 5x 2 - x - 4 = 2 8.) Write each of the following as complex numbers in standard form. Show all necessary work. (2-5 i) + (3 + i) (2-5 i) - (3 + i) (2-5 i)(3 + i) d.) 2 5i 3 i e.) i ) There are three consecutive odd numbers whose product is Write an equation, in one variable, representing the above statement. Using your calculator, solve the equation to find the three numbers. 10.) A farmer has 400 feet of fencing. He wants to create a rectangular pasture. Write a function, A(x), that gives the area, A, as a function of the length, x. Find the dimensions of the rectangle that gives the largest area he can enclose. Find the largest area he can enclose. 11.) Solve the following inequality. Give your answer in graph form. 2x - 3 < 5

4 12.) Solve the following inequality. x 2 - x - 21 < 9 Exam #3 1.) Without using your calculator, solve the following equation for x. x 3 - x 2-64x + 64 = 0 2.) Bubba can do the job in 4 hours and Billy Bob can do it in 6 hours. Assuming Bubba and Billy Bob work at the same speed whether they are working alone or together, how long will it take them to do the job together? 3.) Use your calculator to graph the following equation. Fill in the blanks on the table to show the window you use. Use some method to make horizontal and vertical units equal. (y - 9) 2 = 10 - x 2 xmin xmax ymin ymax 4.) Solve without using your calculator. 5.) Solve without using your calculator. 6.) Does the following function have a slant asymptote? If so, find it. f(x) = 7.) Solve the following polynomial inequality. x 3-5x 2-3x + 9 < 8

5 8.) Consider the following table of values. x y d.) Draw a scatter plot of the data. Write the cubic function that best fits the data. Write the power function that best fits the data. Tell whether the function from or fits the data better. Give numerical reasons for your answer. e.) Draw the better of the two function from and on your scatter plot from. 9.) Solve without using your calculator. Real numbers only. x 2 x 1/ ) No calculator. Find the exact solution(s) for x 3 3x ) No calculator. Find the exact solution(s) for x 2 2 2x ) Consider f(x) =. Draw the graph and fill in all of the blanks below. If Exam #4 something does not exist, write "DNE." x-intercept(s) y-intercept(s) local maximum d.) local minimum e.) interval(s) where increasing f.) interval(s) where decreasing g.) domain h.) range i.) absolute maximum j.) absolute minimum k.) horizontal asymptote l.) vertical asymptote(s) m.) slant asymptote n.) the graph 1.) Consider the following table of values. x y Draw a scatter plot of the data.

6 d.) Write the logarithmic function that best fits the data. Draw the function from on your scatter plot from. Does the function fit the data well? Why? 2.) No calculator. Find the exact solution(s) for x 2 2 2x 3. 3.) Solve the given equation exactly. No calculator. All work must be shown. 4 2x-3 = 8 5x+1 4.) Suppose you invest $8000 at an interest rate of 3.25%. Find the balance after 5 years if the interest is compounded quarterly. Be sure to write down the formula you are using. 5.) Solve the equation without using your calculator. 7 2x-4 = 70 6.) The population of a town was 230 in It was 460 in What is the population in 2012 if the population continued to grow exponentially? 7.) Without using your calculator, solve following the equation. log log 4 2x = 3 8.) Use your calculator to solve the following equation. NOTICE THAT THE BASES ARE NOT THE SAME. Tell me what you entered into your calculator and how you got your answer. log 4 x + log 7 x = 5 For #9-10 you will be solving the following system of equations. BE SURE TO DO IT THE WAY YOU ARE TOLD TO DO IT IN EACH PROBLEM AND SHOW ALL NECESSARY WORK!!! 2x - y = 4 x + 3y = 9 9.) Solve the system of equations without your calculator. Use the method of substitution. 10.) Solve the system of equations without your calculator. Use the method of elimination.

7 11.) Solve the given equation exactly. No calculator. All work must be shown. 2 2x-3 = 2 5x+1 12.) Solve the given equation. 4 2x-3 = 7 5x+1 13.) Suppose there is a base, a, with the following logarithms. log a 2 =.4307, log a 3 =.6826, log a 7 = Find the following logarithms. log a 6 = log a 49 = log a 3.5 = Final Exam 1.) Solve the following equation by factoring. No calculator. x 2-5x - 6 = 8 2.) Solve the following equation by the quadratic formula. No calculator. 3x 2 - x - 7 = 8 3.) Solve the following equation exactly. No calculator. x 2 x 1/ ) Solve the given equation exactly. 8 3x-1 = 4 2x+3 (no calculator) 5.) Solve the given equation exactly. log 2 x + log 2 (x - 4) = 2 (no calculator) 6.) Solve the following equation. You may use your calculator. x 3.2-4x = 0 7.) Use your calculator to find both solutions to the equation 2 (x+1)/5 - log 2 (25x) = 0. 8.) Solve the following system of equations without your calculator. Use the method of elimination. x 2y = 6 2x + y = 7

8 9.) Consider the following data points. x y Find the linear function that best fits the data. Tell whether the line fits the data well, giving an explanation using the correlation coefficient. 10.) Graph the following function. Fill in all of the following. 2 x x 6 f ( x) 2 3x 3 x-intercept(s) horizontal asymptote(s) local minima domain GRAPH y-intercept(s) vertical asymptote(s) local maxima 11.) Given the following table of values, find the exponential function that best fits the data. Discuss whether or not it fits the data well. x y ) Write each of the following as complex numbers in standard form. (1-3 i) + (2 + 2 i) (1-3 i)-(2 + 2 i) (1-3 i)(2 + 2 i) d.) 1 3i 2 2i e.) i ) Solve the following inequality x 2 - x - 6 < 6. No calculator. 14.) Solve the following equation. No calculator. log 6 x + log 6 (x-1) = 1 15.) No calculator. Find the exact solution(s) for x 2 2 2x 3.

9 16.) You put $2000 in the bank at 2.5% interested compounded quarterly. Showing all work, determine how much money you will have after 3 years. 17.) Solve the following equation for ALL solutions. No calculator. x 4 - x 2-12 = 0 18.) Find four consecutive even integers (even integers are numbers like 2, 4, 6,... ) whose product is BE SURE TO SHOW THE EQUATION IN ONE VARIABLE THAT YOU USE TO SOLVE THE PROBLEM. 19.) Solve the inequality 3-5x > ) The population of a colony of mosquitoes obeys the law of exponential growth. Suppose there are 1000 mosquitoes initially and there are 1800 after 1 day. What is the size of the colony after 2 weeks?