MAT141 Test 1 Review FALL 2010 1 MAT141 1. Find the slope and y-intercept of8 1 0xy. 2. Use the table to answer questions a-f. X Y1 Y2 -3 9 -3 -2 4 -1 -1 1 1 0 0 3 1 1 5 2 4 7 3 9 9 a. What is the average rate of change of Y2 from122 to 3xx? b. What equation corresponds to the data for Y2? c. For what value(s) of x is Y1=Y2? d. Does the graph of Y2 pass through the origin? e. At what point(s) do Y1 and Y2 intersect? f. What is the average rate of change of Y1 from120 to 1xx? 3. Find the equation of a vertical line through the point (6,-2). a. x = 6 b. y = 6 c. x = -2 d. y = -2 4. Find the equation of a line through the point (3,2) and perpendicular to the line y = 2x. a. 27yx b. 172yx c. 1722yx d. 1722yx 5. Is the function32()f x x x odd, even, or neither? a. odd b. even c. neither 6. Find the difference quotient ( ) ( )f x h f xh if2( ) 4 2f x x x. 7. If 2 2 , 2()4 5 , 2xxfxxx what is f (-4)?MAT141 Test 1 Review FALL 2010 2 MAT141 8. Which of the following defines y as a function of x? a. 224xy b. 24xy c. x = -3 d. 2xy 9. Find the equation of a line through the point (4,-5) and parallel to the line y = 2. a. y = 2x-8 b. y = 2x-13 c. y = -5 d. y = 4 10. Find the equation of a line whose x-intercept occurs at x = -4 and whose y-intercept occurs at y = 5. 11. If( ) 2 3f x x, what is f(t - 1)? a. 2t - 1 b. 2t + 2 c. 2t + 1 d. 2t + 4 12. Find the equation of a line that passes through the point (3,1) and is perpendicular to the line x = 5. a. x = 3 b. x = 1 c. y = 3 d. y = 1 13. Which of the following gives the equation of the straight line which crosses the y-axis at the point 4,0 and has a slope of6 ? a. 46xy b. 46xy c. 64xy d. 64xy 14. What is the slope of the straight line graphed on the coordinate plane below? You may assume that each tick mark represents one unit. y xMAT141 Test 1 Review FALL 2010 3 MAT141 15. Answer questions a-j for each of the graphs shown below. You may assume that each tick mark represents one unit. ()y f x ()y g x a. Explain why both graphs represent functions. b. Find the x- and y-intercepts for both graphs. c. What is the range of g(x)? d. On what interval(s) is g(x) decreasing? e. On what interval(s) is f(x) increasing? f. Is g(x) odd, even, or neither? What about f(x)? g. Is f(2) positive or negative? Is g(4) positive or negative? h. Find the relative max and/or min of both functions. 16. Let 21( ) , ( )2f x x g xx. Find ( )( ),( )( )f g x g f x and the domain of each. 17. Let 2( ) 3, ( ) 2 1f x x g x x. Find ( )( ),( )( )f g x g f x and the domain of each. 18. Describe the transformation from ()f x x to( ) 3 1f x x. a. The graph is shifted left 3 units and down one unit. b. The graph is shifted right 3 units and down one unit. c. The graph is shifted left one unit and down 3 units. d. The graph is shifted right one unit and down 3 units. x x y yMAT141 Test 1 Review FALL 2010 4 MAT141 19. Which of the following is an even function? a. 2( ) 2 5 1f x x x b. ( ) 3 1f x x c. 2( ) 3f x x d. ( ) 2 3f x x 20. Write the equations for the following transformations of 3()f x x. a. The graph is moved down 4 units and reflected across the x-axis. b. The graph is moved left two units and stretched by a factor of 2. c. The graph is moved to the right one unit and up one unit. d. The graph moves three units left, down one unit, and is reflected across the