Math 245 Practice Test #3

Transcription

1 Math Practice Test #3 Name Show all work neatl and sstematicall for full credit. Graph the function. 1) Given: f() = ) Given: f() = 3-1 Horizontal Asmptote: b. Is f a one-to-one function? Eplain. Graph. Show at least 3 points on the graph. c. Find the inverse of f Use the definition of inverses to determine whether f and g are inverses. ) f() = +, g() = 1 - d. What is the domain and range of inverse function? e. Graph f and its inverse on the same aes

2 Graph the function. ) Given: f() = - 3 7) Given: f() = - b. Is f a one-to-one function? Eplain. Horizontal Asmptote: Graph. Show at least 3 points on the graph. c. Find the inverse of f d. What is the domain and range of inverse function? Solve the equation. ) 3( - ) = 79 e. Graph f and its inverse on the same aes. ) e - 1 = (e)

3 8) Given: f() = + 1, 0; Find the future value. 9) $383.9 invested for 1 ears at % compounded monthl b. Is f a one-to-one function? Eplain. Evaluate the logarithm. ) log 1 c. Find the inverse of f. Write in logarithmic form. 11) - = 1 Solve the equation. 1) log 1 = - d. What is the domain and range of inverse function? e. Graph f and its inverse on the same aes. 13) log1/3( + ) = Use the properties of logarithms to rewrite the epression. Simplif the result if possible. Assume all variables represent positive real numbers. 1) loga() 3

4 Write the epression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with a 1 and b 1. 1) (loga - loga ) + loga z 17) Given: f() =log3 (-3) + ; b. Write the equation of vertical Asmptote. 1) Given: f() =log1/ ( + 1) ; c. graph f. Show at least 3 points. b. Write the equation of vertical Asmptote. c. graph f. Show at least 3 points Graph the polnomial function. Factor first if the epression is not in factored form. 18) f() = 3( + )( + 1) - - -

5 19) f() = ( + ) Use the intermediate value theorem for polnomials to show that the polnomial function has a real zero between the numbers given. 1) f() = ; 1 and - - Use the change of base rule to find the logarithm to four decimal places. ) log7 3 3) log 3 0) f() = -3( + )( - 1) - - Find a polnomial function f() of least possible degree having the graph shown. ) - (-1, 0) (1, 0) - (0, -) -

6 ) Given: f() = Find all zeros. ) Given: f() = Find all zeros. State all -intercept. State all -intercept. State the -intercept. State the -intercept. What is the end behavior? What is the end behavior? Graph the function, f. Graph the function, f

7 Sketch the graph of the rational function. 7) f() = ) f() = ( - )( - 1) Vertical Asmptoe: Vertical Asmptoe: Horizontal Asmptote or Oblique Asmptoe: X-intercpet: Horizontal Asmptote or Oblique Asmptoe: X-intercpet: -intercept: -intercept: Graph the function f. Graph the function f. 7

8 9) f() = Find an equation for the rational function graph. 30) 3 1 Vertical Asmptoe: Horizontal Asmptote or Oblique Asmptoe: X-intercpet: -intercept: 31) 3 1 Graph the function f Solve the problem. Round our answer to two decimal places. 3) The distance an object falls when dropped from a tower varies directl as the square of the time it falls. If the object falls 1 feet in 3 seconds, how far will it fall in 1 seconds? 8

9 Solve the problem. 33) The weight of a person on or above the surface of the earth varies inversel as the square of the distance the person is from the center of the earth. If a person weighs 180 pounds on the surface of the earth and the radius of the earth is 3900 miles, what will the person weigh if he or she is miles above the earth's surface? Round our answer to the nearest hundredth of a pound. Solve the problem. Round to the nearest tenth unless indicated otherwise. 3) At a fied temperature, the resistance R of a wire varies directl as the length l and inversel as the square of its diameter d. If the resistance is 0. ohm when the diameter is 1 mm and the length is 30 cm, what is the resistance when the diameter is mm and the length is 170 cm? Asmptotes: 7-3) h() = a. find the vertical asmptote. b. Find the horizontal asmptote or oblique asmptote. 9