2.) Find an equation for the line on the point (3, 2) and perpendicular to the line 6x - 3y = 1.

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1 College Algebra Test File Summer 007 Eam #1 1.) Find an equation for the line that goes through the points (-5, -4) and (1, 4)..) Find an equation for the line on the point (3, ) and perpendicular to the line 6-3y 1. 3.) Consider the points (1, -4) and (-5, ). a.) Find the distance between the two points. Find the midpoint of the line segment connecting the two points. 4.) Find the domain of the function 3 f ( ) ) Consider the following table of values y a.) 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 a.). Does the line fit the data well? Give a reason for your answer. 6.) Suppose Use your calculator to find one positive and one negative solution to the equation. Give every decimal place that your calculator gives. 7.) No calculator. Solve the following equation by factoring. Eact answers only ) No calculator. Solve the following equation by the quadratic formula / 9.) No calculator. Solve the following equation eactly ) Let f() Find the verte and all intercepts. Graph the function. 11.) No calculator. Solve this equation by hand. Eact Answer Only!!!

2 1.) Find an equation for the circle with center at (3, -3) and radius ) Find the center and radius for the circle with equation y - y ) No calculator. Find the eact solution(s) for Eam # 1.) Solve the inequality. 5-3 > 7.) Solve the following inequality. Give your answer in inequality form. ( 3)( + ) ) Solve the following inequality. Give your answer in graph form. 3 - < 11 4.) Solve the equation eactly ) Solve the equation eactly ) Consider the function f() Use your calculator to find the following. a.) any local (relative) maima. any local (relative) minima. any -intercepts any y-intercepts e.) domain f.) range g.) graph 7.) For each of the following functions, determine if the function has origin symmetry, y-ais symmetry, or neither. Show your work. ("My calculator told me so" is NOT sufficient.) a.) f() f ( ) f ( ) ) Suppose the graph shown is the graph of f(). On the same set of aes, show the graph of g() - f( + 3) + 4.

3 9.) Consider the function f() Use your calculator to find the following. a.) e.) any -intercepts any y-intercepts domain range graph 10.) Give the graph of f() ) Graph the following function., f ( ) + 1, < ) The number of rare ducks in the Wilmot Zoo varies. The population between 1990 and 1998 is described by the function N(t) t 3-7t + 84t + 416, where t 0 corresponds to When in this 8-year period did the population peak, and when was it at its lowest? 13.) Suppose f is a function with f() 5. Eplain why f cannot have symmetry with respect to the -ais. 14.) Consider the following table of values y a.) Draw a scatter plot of the data. Write the third degree polynomial function that best fits the data. Draw the function from on your scatter plot from a.). Does the function fit the data well? Why? Eam #3 1.) Graph the following function. Find all of the following.

4 f ( ) intercept(s), y-intercept(s), does it have slant asymptote, horizontal asymptote(s), vertical asymptote(s), local minima, local maima, absolute maimum, absolute minimum, domain, range, does it have -ais symmetry, does it have y-ais symmetry, does it have origin symmetry, intervals where increasing, intervals where decreasing GRAPH.) Suppose f() 3 + and g() - 1. a.) Find (f - g)(3). Find (f g)(). Find (g g)(). f Find the domain of (). g 3.) Does f() have an inverse function? Give a reason for your answer. If it has an inverse, find it. 4.) Write each of the following as comple numbers in standard form. a.) (1-3 i) + ( + i) (1-3 i) - ( + i) (1-3 i)( + i) 1 3i + i e.) i ) Graph f() Be sure to include the asymptote(s). 6.) The formula P 14.7e 0.1 gives the average atmospheric pressure, P, in pounds per square inch, at an altitude miles above sea level. a.) Find the atmospheric pressure for an altitude for.8 miles. Round your answer to the nearest hundredth. If the atmospheric pressure around you is 4.6 pounds per square inch, how far above sea level are you? [hint: I've told you P, you need to find.] 7.) Solve the given equation eactly. No calculator. All work must be shown ) Solve the equation using your calculator ) Consider the following table of values.

5 y a.) Draw a scatter plot of the data. Write the eponential function that best fits the data. Draw the function from on your scatter plot from a.). Write the third degree polynomial function that best fits the data. e.) Draw the function from on your scatter plot from a.). f.) Which function, the one from or the one from fits the data better. Why? g.) Based on the eponential function, what will y be when 5? 10.) Suppose you invest $8000 at an interest rate of 5.4 percent. Find the balance after 4 years if the interest is compounded quarterly. Be sure to write down the formula you are using. 11.) Without using your calculator (be sure to show all work), solve for in each of the following. a.) log 3 log 16 log ) Use your calculator to solve the following equation. e log ( + 1) ) 13.) Without using your calculator, solve following the equation. log log 3 14.) Use your calculator to solve the following equation. log 3 + log 5 Eam #4 1.) Do not use your calculator. Solve the following system of equations. Use the method of elimination. + y y 19.) Solve the following system of equations. Use the method of substitution. + y y 19 3.) Solve the following system of equations. Use your calculator and the method we used involving matrices. Show the matrices you use. + y y 19

6 4.) Solve the following system of equations WITHOUT USING YOUR CALCULATOR AT ALL. Show all of your work. y - 1 y ) Use your calculator to find all solutions to the following system of equations. Give at least 4 decimal places. ln( + 5) + y 3 + y 6.) Graph the solution to the following system of inequalities. - y < 4 + y > 4 7.) Given a n n / (n - 1), find the following. a.) a 1 a a 3 S 3 (hint: your calculator is your friend) 8.) Consider the arithmetic sequence whose first two terms are a 1 3 and a 7. DO NOT USE YOUR CALCULATOR. SHOW ALL WORK. a.) Find the 3-rd term. Find the sum of the first 3 terms. 9.) Find the second, third and fourth term of the recursively defined sequence below. a 1 a n a n-1 + 3, for n > 10.) Given an arithmetic sequence with a 1 and a 3 8, find the following without using your calculator. Be sure to show your work. a.) a a 15 S ) Consider the geometric sequence whose first two terms are a 1 3 and a 6. DO NOT USE YOUR CALCULATOR. SHOW ALL WORK. a.) Find the 3-rd term. Find the sum of the first 3 terms. 1.) Consider the infinite geometric series whose first two terms are a 1 3 and a. Find the sum if it eists. If it does not eist, tell why not. 13.) Find the maimum and minimum values of the function and the points at which they occur, subject to the given constraints. f + 5y 4 + y < 1 + y < 6 > 0 y > 0

7 Final Eam 1.) Suppose f() 3 + and g() - 1. a.) Find (f - g)(3). Find (g g)(). f Find the domain of (). g.) This problem refers to the following table which gives population data for Rogers, Arkansas. Use 0 to represent 1900, 10 for 1910, etc. year y,80 3,318 3,554 3,550 4,96 5,700 11,050 17,49 4,69 38,89 Do the following a.) Find an equation for the eponential function that best fits this data. Is it a good fit? Why or why not? Based on the eponential model, what would the population of Rogers be in 007? 3.) Consider the arithmetic sequence with a 1 4 and a 3 8 (pay CLOSE attention to the subscripts). Find the following: a.) a 85 S 85 4.) Using factoring, and no calculator, solve the equation ) Solve the following equation by the quadratic formula ) Without using your calculator, solve the equation eactly ) Solve the following inequality. 7-5 < 10 8.) Solve the following inequality > 16 9.) Solve the following equation ) Find an equation for the line passing through the points (, -5) and (4, 7) ) Use your calculator to solve the following equation. e 3 log( + 3) 1.) 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?

8 13.) Use algebraic methods (not your calculator) to determine whether or not f() /( + 1) has symmetry with respect to: a.) the y-ais the origin 13.) Graph the following function. Fill in all of the following. 6 f ( ) 3 3 -intercept(s), y-intercept(s), horizontal asymptote(s), vertical asymptote(s), domain, slant asymptote(s), local minima, local maima, graph 15.) Suppose the graph in the left hand grid is f(). On the right hand grid, graph g() f(+3) ) Suppose you invest $8000 at an interest rate of 5.4 percent. a.) Find the balance after 4 years if the interest is compounded quarterly. Be sure to write down the formula you are using. Find the balance after 4 years if the interest is compounded continuously. Be sure to write down the formula you are using. 17.) Solve the following equation by hand. Eact Answer Only!!! ) Solve the following equation by hand. Eact Answer Only!!! log 6 ( - 1) + log 6 () 1 19.) You roll two standard si-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 ( +1) - log ) Solve the following system of equations (no calculator) using the method of elimination. 4 + y y 5

9 .) Graph the solution to the following system of inequalities - y 5 + y 4 3.) Solve the following system of equations. You may use your calculator. Tell me what method you used on your calculator y π - e π y ) Consider the following table of values y a.) e.) f.) Draw a scatter plot of the data. Write the logarithmic function that best fits the data. Draw the function from on your scatter plot from a.). Write the third degree polynomial function that best fits the data. Draw the function from on your scatter plot from a.). Which function, the one from or the one from fits the data better. Why? 5.) Consider the geometric sequence with a 1 4 and a. Find the following (if they eist): a.) a 0 S 0 the sum of the infinite series

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