Sample Questions to the Final Exam in Math 1111 Chapter 2 Section 2.1: Basics of Functions and Their Graphs

Transcription

1 Sample Questions to the Final Eam in Math 1111 Chapter Section.1: Basics of Functions and Their Graphs 1. Find the range of the function: y 16. a.[-4,4] b.(, 4],[4, ) c.[0, ) d.(, ) e.. Find the domain of the function: f ( ). a.(-,] b.(, ) c.[, ) d.[, ) e.. Use the vertical line test to determine in which case y is a function of. a. c. d. e. 4. Use the vertical line test to determine in which case y is a function of. a. of these b. c. d. e. None 5. Which of the following is NOT a function? a. b. c. d. e. 6. The graph of a function y f is indicated. Find all values of for which f 0. a. 1 b. 0 c. 1, 0 d. 1, e. 0, y Find the range of g ( ) 1. a. {-1,1} b. (,1) (1, ) c.(, 1) (1, ) d.(, ) e.

2 8. Determine which equation represents y as a function of. a. y 4 b. ( ) y 4 c. y 4 d. y e. 9. Find the domain of f ( ) 1. a. (-, ) b. (, ] [, ) c.(,) d.(,1) e. 10. Given f( ) 58, find f( ). a. -0 b. 8 c. 6 d. 4 e. 11. Given g ga ( ) 1, find ( 1). a b a c a d a e. a..( 1) 1.( ) Given g g g ( ) 5 ( 1), find ( 1) ( ). a b c d e 1 1. Given f( ), find f. 1 a a 1 a 1 a. b. c. d. e. 1-a a1 a1 1a Section.: Functions 1. Use the graph below to give the zeros of the function. a.,-4,-7 b.,0, 4,7 c.11 d., 4,7 e.. The graph of a function y f is indicated. Find the value of 4 a. 0 b. 1 c. d. 5 e.1 f.. Give the intervals on which the function is increasing. a. -1,1 b. 1,0 1, c., d., 1 1, e. 0,1 4. Give the relative maimum value of the function a..5 b c.0.14 d.6.5 e. f if 5. Given f( ), find f( ). 4 if a. 16 b. c. 16 d. e. 6. Determine whether the function f ( ) 7 - is even, odd, or neither. a. even b. odd c. neither

3 Sections. and.4 : Linear Functions and Slope 1. Find the slope of the line containing (,5) and (4,-). 1 7 a. -7 b. c. d. e Find the -intercepts of the line containing (1,10) and (-5,-). a. (0,-4) b. (0,8) c.( 4,0) d.( 5, ) e.. Find the slope of the line which is perpendicular to the line -y = -4. a. - b. c. d. e If the line y m b is parallel to the line 4y, find m. 4 1 a. - b. c. d. e Which of the following represents a horizontal line? a. y-=0 b. y 0 c. 0 d. 0 e. 6. Which of the following has a negative y-intercept? a. -y=0 b. y c. y d. y 0 e. 7. The equation of the line containing (-,1) and (-,-1) is a. y+1=0 b. y1 0 c. y 0 d. 0 e. 8. Find the equation of the line with -intercept -4 and y-intercept. a. -4y=-1 b. 4y 1 c.4y 1 d.4y 1 e. 9. Find the equation of the line containing the origin and perpendicular to the line 68y. a. +4y=0 b. 4y 0 c.4 y 0 d.1 0 e. 10. Find the equation of the line passing through (,-) and parallel to the line 4y 5. a. 4+y=-1 b. 4y 15 c.4 y 18 d.4y 6 e. 11. Find the equation of the line with slope and -intercept -5. a. -y=5 b. y 15 c. y 5 d. y 5 e. 1. Find the equation of the line passing through (0,4) which is perpendicular to the line y 7. a. +y=4 b. y 1 c. y 4 d. y 4 e. Section.5 : Transformations of Functions 1. If the graph of f ( ) is shifted and the new verte is (,-), find the transformed function. a b f c f d e. f()=(-). ( ) ( ). ( ) ( ).( )... Match the graph with the correct function. ( a) f( ) 4 5 ( b) f( ) 4 5 ( c) f( ) 4 5 ( d) f( ) 4 5. Which of the following could be the graph of y 1?

4 a) b) c) d) e) 4. The graph of y is shifted 5 units to the left, reflected over the -ais, stretched vertically by a factor of, and shifted down 7. Give the equation of the resulting function. a. y 5 7 b. y 5 7 c. y 5 7 d. y 5 7 e. 5. The graph of a function resembles the graph of y, but has been shifted up units and passes through the point 1, 5. Which of the following could be the equation for the graph? a. y b. y c. y d. y e. Section.6 : Combinations of Functions 4 1. Give the domain of the function f a. 4 b. 5 or c.{ is a real number} d. or 5 e.. Give the domain of the function f 4. a. { is a real number} b. 0 c. 4 d. e.. Give the domain of the function f a. 0 b. c. d. e If f ( ), find ( f f)( ) a. 4 b. 6 c. 4 d. 9 e Given f ( ) 4 and g( ) 1, find ( f g)( ). a. 5- b. c. ( ) d.0 e. 6. Given f ( ) 6 and g( ) 1, find ( f g)( ). a b c d e 7. Given f ( ) and g( ) 1, find ( fg)( ). a. +1 b. c.1 d. 1 e. f 8. Given f ( ) and g( ) 1, find ( ). g

5 1 a. b. c. d.41 e Given f ( ) and g( ) 5, find ( g f)( ). 10. Given a b c d e. (+5) f g f g ( ) and ( ), find ( )( ). a b c d e Section.7: Inverse Functions 1 1. Find the inverse function of g ( ) y1 1 1 a. g ( ) b. g ( ) c. g ( ) 1 d. g ( ) 8 1 e. 8. If f ( ), which of the following is a point on f 1 ( )? a. (-,6) b. (6,) c.(6, ) d.(, 6) e. 1. Find the inverse function of f( ) ; a. f ( ) b. f ( ) c. f ( ) d. f ( ) e. 4. Which of the following has an inverse function? a. b. c. d. e.

6 5. Find the inverse of the function shown on graph. a. b. c. d. e. Section.8: Equation of a circle and Distance and Midpoint Equations 1. Find the distance between the points:, 1 and, 4. a..16 b..8 c d. 5.8 e. 5, and 9,.. Find the midpoint point: b a.,0. 5,9 c., d. 8,1 e.. Determine the equation of the circle in standard form with radius and center (-1,). a. 1 y b. 1 y 4 c. 1 y d. 1 y 4 e. 4. Find the center and radius of the circle: ( ) ( y 4) 5. a. Center : (, 4); r 5 b. Center : (, 4); r 5 c. Center : (, 4); r 5 d. Center : (, 4); r 5 e.