Math Review Chapter 1

Transcription

1 Math 60 - Review Chapter Name ) A mortgage on a house is $90,000, the interest rate is 8 %, and the loan period is 5 years. What is the monthly payment? ) Joan wants to start an annuity that will have $890,000in it when she retires in 5 years. How much should she invest annually in her annuity to do this if the interest is 8% compounded annually? Use the graph to answer the question appropriately. 3) The population of rabbits varies with the season due to migration, birth and death. The number, N, of rabbits during month x on a certain midwestern farm can be estimated with the following graph, where x = corresponds to January, x = corresponds to February, and so on. How many rabbits left the area or died between September and October? Evaluate the function. 4) Find f(k - ) when f(x) = 5x - 3x ) Find f(-) when f(x) = A) 3 6x 4x - 3. B) 6 C) 4 D) Graph the function. 6) f(x) = x3-5 Determine if the equation represents a function. 7) x = y + 6 Graph the function. 5x +, 8) f(x) = x, 4x -, for x < -, for - x 3, for x > 3

2 9) The cost of renting a branch chipping machine is a function of the hours it is rented and is defined by C(x) = $50, for x 4, $ x, for x > 4, x is the number of hours rented. If the rental cost was $435.00, how many hours was the machine rented? 0) The following graph shows the stock price of a new internet company over the first 8 months after the initial public offering of its stock y Stock Price (in dollars) x Month Approximately in which month(s) did the stock price reach $60? Write the interval notation for the graph. ) r r + t Write interval notation for the set. ) {xv x 6} Find the domain and the range for the function. 3) State the domain of the given function. 4) f(x) = 3x + x - 3

3 x 5) y = x - 6 6) f(x) = 7x + 9 7) f(x) = x + 4 Find the range of the function. 8) f(x) = x3-9) A toilet manufacturer has decided to come out with a new and improved toilet. The fixed cost for the production of this new toilet line is $6,600 and the variable costs are $69 per toilet. The company expects to sell the toilets for $50. Formulate a function P(x) for the total profit from the production and sale of x toilets. Determine the vertex of the parabola. Solve. 0) y = 5x - 50x + 34 ) r + 3r = 9 Convert to an expression with a rational exponent. ) 3 a Convert to an expression using radical notation. 3) y-7/5 Evaluate the expression. 4) 044/5 Find the domain. x - 9 5) f(x) = x - 5x ) When the leaves fall off maple trees in the fall, we can estimate the number of leaves per square foot under the tree with the following function: y = 5.x5/9 -, where x is the number of days after October 0. Predict the density of the leaves on November 0. 3

4 Find the equilibrium point for the supply and demand curves. Round answers to two decimal places. 7) D(p) = 840-0p, S(p) = p Quantity (q) Price (p) S D 8) D(p) = 4 p, S(p) = p Quantity (q) Price (p) S D Use the ZERO or the INTERSECT feature on your calculator to approximate all the zeros of the function to three decimal places. 9) f(x) = 8 + x3-4 30) The information in the chart gives the salary of a person for the stated years. Model the data with a linear function using the points (, 4,00) and (3, 6,00). Year, x Salary, y 990, 0 $3,500 99, $4,00 99, $5,00 993, 3 $6,00 994, 4 $7,00 3) The height of an object dropped from a tall building is given by the table, where t is the elapsed time in seconds and h is the height in feet. t h Find a quadratic function that fits the data. 4

5 Provide a short answer. 3) Consider the linear function f(x) = 5x + 0. What is the domain and range of this function? Now, suppose the function represents the relationship between studying time and grades on an exam. The variable x represents the number of hours spent studying and f(x) represents the grade on the exam. Does this change the domain and range? If so, what is the new domain and range and why is it different? 5

6 Answer Key Testname: CHAPT ) $87.0 ) $,74. 3) 3 4) 5k - 3k + 5 5) D 6) 6 y -6 6 x 7) No 8) -6 0 y -5 5 x -0 9) 9.5 hours 0) The 8th month ) (r, r + t] ) (-«, 6] 3) Domain = (-«, «), Range = [-, «) 4) (-«, «) 5) (-«, 6) U (6, «) 6) (-«, «) 7) [-4, «) 8) All real numbers 9) P(x) = 8x ) (5, 9) ) -3 ± 3 5 ) a-/3 3) 5 y7 4) 56 6

7 Answer Key Testname: CHAPT 5) {xvx is a real number and x 6 and x 9} 6) 34 leaves per square foot 7) (9.00, ) 8) (.83,.4) 9) x = 30) y = 950x + 3,500 3) h(t) = -6t ) The domain is all real numbers and the range is the set of all real numbers. In the context of exam grades, the domain and range both become the set of nonegative real numbers. In this context, times and grades less than zero do not make sense. 7