Math 1101 Test 2 Practice Problems

Transcription

1 Math 1101 Test 2 Practice Problems These problems are not intended to cover all possible test topics. These problems should serve as on activity in preparing for your test, but other study is required to fully prepare. These problems contain some mulitple choice question, please consult with your instructor for particular details about your class test. Use factoring to solve the equation. 1) 3x2-15x + 18 = 0 Find the x-intercepts. 2) y = 4x2-6x Use the quadratic formula to solve the equation. 3) p2 + 5p - 5 = 0 A) -5 ± B) C) -5 ± 3 5 D) Use a graphing utility to find or approximate solutions to the equation. If necessary, round your answers to three decimal places. 4) 4n2 = -6n - 1 A) , B) , C) 0.151, D) , Find the exact solutions to the quadratic equation in the complex numbers. 5) x2 + x + 2 = 0 1

2 6) A ball is thrown downward from a window in a tall building. The distance traveled by the ball in t seconds is s = 16t2 + 32t, where s is in feet. How long (to the nearest tenth) will it take the ball to fall 96 feet? A) 2.6 sec B) 2.4 sec C) 1.4 sec D) 1.6 sec Graph without the use of technology. 7) f(x) = 1 x - 4 8) y = x - 2 Find the requested value. 9) f(6) for f(x) = 3x + 1 if x < 1 6x if 6 x 9 6-6x if x > 9 A) -30 B) 4 C) 36 D) 55 Determine if the function is concave up or concave down in the first quadrant. 10) y = x4/3 A) Concave up B) Concave down 2

3 Determine if the function is increasing or decreasing over the interval indicated by drawing a sketch of the graph using your knowledge of the graph of the power functon y=x^4. 11) y = -3x4 ; x < 0 A) Increasing B) Decreasing Fill in each blank with the appropriate response. 12) The graph of y = -5(x - 4)2 + 7 can be obtained from the graph of y = x2 by shifting horizontally units to the, vertically stretching by a factor of, reflecting across the -axis, and shifting vertically units in the direction. Write the equation of the graph after the indicated transformation(s). 13) The graph of y = x is shifted 2 units to the left. Then the graph is shifted 3 units upward. A) y = x B) y = x C) y = x D) y = 3 x + 2 Determine whether the graph of the given equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. 14) f(x) = -8x3 + 4x Determine whether the function is even, odd, or neither. 15) y = x2 + 3 A) Odd B) Even C) Neither 16) A furniture manufacturer decides to make a new line of desks. The table shows the profit, in thousands of dollars, for various levels of production. Number of Desks Produced Profit (Thousands) Find a quadratic function that best fits the data, and use the model to predict the profit if 450 desks are made. A) Almost $44,000 B) Almost $42,000 C) Just over $40,000 D) Just under $45,000 17) The percent of people who say they plan to stay in the same job position until they retire has decreased over recent years, as shown in the table below. Year Percent Find a power function that models the data in the table using an input equal to the number of years from A) y = x B) y = x C) y = x D) y = x

4 Provide an appropriate response. 18) The following table has the inputs, x, and the outputs for three functions, f, g, and h. Use second differences to determine which function is exactly quadratic, which is approximately quadratic, and which is not quadratic. x f(x) g(x) h(x) ) Determine whether a linear or quadratic function would be a more appropriate model for the graphed data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the coefficient of x2 should be positive or negative. DENTAL FLOSS USE People (in Millions) Years since 1990 A) Linear; positive B) Quadratic; negative C) Linear; negative D) Quadratic; positive Find the specified domain. 20) For f(x) = 2x - 5 and g(x) = x + 9, what is the domain of f g (x)? A) [0, ) B) [9, ) C) (-9, 9) D) (-9, ) Find the requested composition of functions. 21) Given f(x) = 4x2 + 6x + 7 and g(x) = 6x - 8, find (g f)(x). 4

5 Find the requested function value. 22) Find (g f)(-4) when f(x) = 4x + 5 and g(x) = 4x2-5x - 3. A) 9 B) 536 C) 329 D) 8 For the functions f and g, find the requested value. 23) Use the graphs of f and g to find (g f)(-3). y = f(x) y = g(x) 24) At Allied Electronics, production has begun on the X-15 Computer Chip. The total revenue function is given by R(x) = 60x - 0.3x2 and the total cost function is given by C(x) = 10x + 12, where x represents the number of boxes of computer chips produced. The total profit function, P(x), is such that P(x) = R(x) - C(x). Find P(x). A) P(x) = -0.3x2 + 50x - 12 B) P(x) = 0.3x2 + 50x - 24 C) P(x) = 0.3x2 + 40x - 36 D) P(x) = -0.3x2 + 40x

6 Decide whether or not the functions are inverses of each other. 25) f(x) = 5 4x + 5, g(x) = x + 4 x Determine whether or not the function is one-to-one. 26) A) Yes B) No 27) f(x) = 8x2-3 A) Yes B) No Determine whether the function is invertible. 28) The function that pairs students' ID numbers with their GPAs. A) No B) Yes Find the inverse of the function. 29) f(x) = 5x - 2 2x - 8 6

7 Graph the function using transfomations of an exponential function's graph with which you are familiar. 30) f(x) = 4(x - 2) ) A computer is purchased for $4800. Its value each year is about 78% of the value the preceding year. Its value, in dollars, after t years is given by the exponential function V(t) = 4800(0.78)t. Find the value of the computer after 7 years. Provide an appropriate response. 32) What are the domain and range for the equation y = 2x? A) Domain: (0, ); range: (, ) B) Domain: (, ); range: (0, ) C) Domain: (, ); range: (, ) D) (, ); range: [0, ) 33) What is one ordered pair that is always on the graph of f(x) = ax? Write the logarithmic equation in exponential form. 34) log = 3 35) ln x = -7 A) x = e7 B) x = ln -7 C) No solution D) x = e-7 Write in logarithmic form ) =

8 Find the value of the logarithm without using a calculator. 37) log A) 6 B) -2 C) 2 D) -6 Graph the function. 38) f(x) = log 2 (x) + 4 Find the inverse of the function. 39) f(x) = 8x A) f-1(x) = logx 8 B) f-1(x) = ln 8x C) f-1(x) = log8 x D) f-1(x) = x8 Solve the equation. 40) log 5 x = -2 A) 3 B) 1 32 C) -10 D) ) A certain noise has an intensity I of Given that decibel level L is related to intensity by L = 10 log I Io, where I o is 10-12, determine the decibel level of the noise. Round your answer to the nearest decibel. A) 69 decibels B) 182 decibels C) 79 decibels D) 8 decibels 8