MAT 141 Fall 2009 In Class Assignments2 To: MAT 141 students Re: In-Class Assignments This is a booklet of In-Class Assignments that we will be working on this semester. Please make sure that you bring this booklet along with your notebook to class each time that we meet. There is an In-Class Assignment for each class meeting. We will be working on these during our class meeting. You may work alone or in groups – whichever way you feel most comfortable. I will come around and help you with the work and answer your questions. I expect that you will show the work in your notebook. I will periodically ask to see your notebook to make sure that you have done the work and that your work is neat. If you must miss a class meeting you will know what we covered in class from the letter that I gave you the first day and you will know that you will be responsible for the In-Class Assignment.3 College Algebra – MAT 141 In Class Assignment 1 Chapter 1 - Section 1 1. Graph 12yx and22yx letting 3, 2, 1,0,1,2,3x. 2. Write a sentence explaining the meaning of a [-20, 10, 2] by [-5, 5, 1] viewing rectangle. 3. Find the intercepts of the graph of the equations below. a. 3 4 12xy b. 24yx 4. Write each of the following English sentences as an equation. a. The y-value is 1 less than twice the x-value. b. The y-value is the square of two less than the x–value. 5. Sketch a graph that depicts the sentence, The cork dropped into the water. 6. a. Does Y1 pass through the origin? b. What is the x-intercept of Y2? c. For which values of x is Y1=Y2? d. The graph of Y2 is in which quadrants? e. The graph of Y1 is in which quadrants? X Y1 Y2 -3 -5 - 9 -2 - 4 - 4 -1 - 3 - 1 0 - 2 0 1 - 1 - 1 2 0 - 4 3 1 - 9 x y x y4 College Algebra – MAT 141 In Class Assignment 2 Chapter 1 – Section 2 1. Determine whether the relation is a function. Identify the domain and the range. a. 3,1 , 5,1 , 7,1 b. 5,0 , 3, 1 , 0,0 , 5, 1 , 3, 2 2. Determine whether the equation represents y as a function of x. a. 234xy b. 21xy c. 2yx 3. Given 2( ) 5 4 ,f x x x find a. (0)f. b. ( 1)f. c. (3)f. d. ()ft. e. ( 1)ft. 4. A graph of a function, f, is shown. Find( 2), (0), 4f f f. Note the scales on the axes. 5. Given ()2xfxx, find a. (2)f. b. (1)f. c. ( 16)f. d. ()fx. e. 23()f. 6. Rewrite the equations below as functions of the first variable in the equation. a. 3 2 4xy b. 3 2 5ts c. 54wz x y5 7. Given the piecewise function22, 1()1 0, 1xxfxxx , find a. (0)f. b. ( 1)f. c. (3)f. d. ( 2)f. e. (1)f. 8. Match the function with the correct graph. I.2 3, -1()3 , 1xxfxxx II 22, -1(), 1xfxxx III24, 2( ) , 2 26 , 2xf x x xxx B) A) C) x y x y x6 College Algebra – MAT 141 In Class Assignment 3 Chapter 1 – Section 3 1. Find and simplify the difference quotient, ( ) ( ),0f x h f xhh, for the following functions. a. ( ) 5 1f x x b. 2( ) 3 2f x x x c. 2()3fxx 2. Sketch the graph of the piecewise function. 21, if 2, if 2 11, if 1xxf x x xx Write a sentence explaining how you know this is a function. What are the domain and range of this function? Find ( 2), (0), (3)and ( 1)f f f f. 3. Sketch the graph of the following functions and determine the approximate intervals on which they are increasing and the intervals on which they are decreasing. Approximate any relative maximum or minimum using the trace and zoom features of the calculator. Then find to 2 decimal places the relative minima and maxima. a. 24f x x x b. 3( ) 9f x x x c. ( ) 7 3f x x d. 2( ) 4f x x 4. Sketch the graph of a function that is always decreasing and ( ) 0fx for all x. 5. Determine algebraically whether the function is even, odd or neither. Verify your answer using the graphing calculator. a. 2( ) 2f x x b. 3( ) 5f x x x c. 2( ) 4f x x x d. 42( ) 3 2 7f x x x7 College Algebra – MAT 141 In Class Assignment 4 Chapter 1 – Sections 4, 5 1. Find the slope of the line passing through the points. a. 2,1 , 3, 5 b. 0, 4 , 2,5 2. Find the slope and y-intercept of each line whose equations are below. a. 32yx b. 39xy c. 24xy 6. Find the x- and y-intercepts of the line whose equation is given below and sketch the line. a. 37xy b. 4x c. 8 2 2y 7. Write the general form of the equation of a line satisfying the given conditions. a. 12,0 ,3m b. 4, 2 , 0m c. 3,2 , is undefinedm d. 0, 3 , 4m 8. Find the slope-intercept form of the equation of the line that passes through the given points. Graph the line on your calculator and verify that the points are on the line. a. 5, 2 , 0,3 b. 5,2 , 6,0 c. 1 2 3 1, , ,2 3 2 6 9. Write the slope-intercept form of the line though the given point (a) parallel to the given line and (b) perpendicular to the given line. a. 3,1 , 4 1yx b. 2, 1 , 2 3xy 10. Find the average rate of change of212( ) 2 from 1to 5f x x x x x.8 College Algebra – MAT 141 In Class Assignment 5 Chapter 1 – Section 6 1. Using the function2()f x x, write a function that has the indicated transformations. Sketch the graph of f and each new function. a. Reflected about the x-axis b. Reflected about the y-axis and shifted down 3 units c. Shifted up 2 units and right 7 units and reflected about the x-axis d. Stretch vertically by a factor of 5 and reflected about the x-axis 2. Using the function()f x x, write a function that has the indicated transformations. Sketch the graph of f and each new function. a. Shifted right 2 units with a horizontal shrink by a factor of 2 b. Stretched vertically by a factor of 3 and shifted to right 5 and down 2 units. c. Reflected about the y-axis with a vertical shrink by a factor of 3 d. Reflected about both the x- and y-axis 3. Explain how the graph of g is obtained from the graph of f. Sketch the graph of both functions. a. 33; 1 2f x x g …