John Jay College of Criminal Justice The City University of New York Department of Mathematics and Computer Science MAT 105 - College Algebra Departmental Final Examination Review Topic #1: Evaluating and Simplifying Algebraic Expressions Evaluate the algebraic expression for the given value or values of the variable(s). 1) y - 7 x 6 x + xy ; x = - 2 and y = 3 1) A) - 17 18 B) 11 6 C) - 1 D) 11 18 2) - b + b 2 - 4ac 2a when a = 5 , b = 14 , and c = - 3 2) A) 1 5 B) - 1 5 C) - 3 D) 3 Simplify the algebraic expressions: 3) ( 12 y + 9 ) + ( 11 y 2 - 6 y + 9 ) 3) A) 11 y 2 + 18 y - 18 B) 29 y 6 C) 11 y 2 - 6 y + 18 D) 11 y 2 + 6 y + 18 4) ( 3 a - 2 b - 5 c) - ( 9 a - 6 b - 7 c) 4) A) - 6 a + 4 b + 2 c B) 12 a - 8 b - 12 c C) - 6 a + 4 b - 12 c D) - 6 a - 8 b + 2 c 5) (x - 11 )( x 2 + 7 x - 5 ) 5) A) x 3 - 4 x 2 - 82 x + 55 B) x 3 + 18 x 2 + 82 x + 55 C) x 3 + 18 x 2 + 72 x - 55 D) x 3 - 4 x 2 - 72 x - 55 6) - 35 x 2 + 28 x + 21 7 6) A) - 5 x 2 + 4 x + 3 B) - 35 x 2 + 28 x + 3 C) - 245 x 2 + 196 x + 147 D) - 5 x 2 + 28 x + 21 7) 20 x 9 y 11 z 9 4 x 4 y 3 z 8 7) A) 5 x 4 y 7 z B) 5 x 5 y 8 C) 5 x 5 y 8 z D) x 5 y 8 z 1
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Topic #1: Evaluating and Simplifying Algebraic Expressions · 2018-12-04 · Topic #1: Evaluating and Simplifying Algebraic Expressions Evaluate the algebraic expression for the given
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John Jay College of Criminal JusticeThe City University of New YorkDepartment of Mathematics and Computer ScienceMAT 105 - College Algebra
Departmental Final Examination Review
Topic #1: Evaluating and Simplifying Algebraic Expressions
Evaluate the algebraic expression for the given value or values of the variable(s).
Determine whether the relation is a function.59) {(-7, -1), (-7, 2), (-1, 8), (3, 3), (10, -7)} 59)
A) Not a function B) Function
Evaluate the function at the given value of the independent variable and simplify.60) f(x) = -3x - 8; f(-2) 60)
A) 22 B) -2 C) 14 D) -11
61) f(x) = x + 11; f(-2) 61)A) -3 B) 3C) 1.73 D) not a real number
Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.62) 62)
A) function B) not a function
63) 63)
A) not a function B) function
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64) 64)
A) function B) not a function
Use the graph to find the indicated function value.65) y = f(x). Find f(-1) 65)
A) -0.2 B) -4.2 C) 4.2 D) 0.2
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Use the graph to determine the function's domain and range.66) 66)
A) domain: (- , )range: [-4, )
B) domain: (- , )range: (- , )
C) domain: [-1, )range: [-4, )
D) domain: (- , -1) or (-1, )range: (- , -4) or (-4, )
67) 67)
A) domain: [0, )range: [0, )
B) domain: [0, )range: (- , )
C) domain: [0, )range: [-1, )
D) domain: (- , )range: [-1, )
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Identify the intervals where the function is changing as requested.68) Increasing 68)
A) (-3, 3) B) (-3, ) C) (-2, ) D) (-2, 2)
69) Constant 69)
A) (-1, 1) B) (2, ) C) (-2, -1) D) (1, 2)
Evaluate the piecewise function at the given value of the independent variable.
70) f(x) = 3x + 1 if x < -1-2x - 5 if x -1
; f(2) 70)
A) -8 B) -9 C) 1 D) -3
Determine whether the given function is even, odd, or neither.71) f(x) = x3 - 5x 71)
A) Neither B) Even C) Odd
72) f(x) = 2x2 + x4 72)A) Odd B) Neither C) Even
73) f(x) = x3 - x2 73)A) Neither B) Odd C) Even
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Topic #11: Slope and Linear Functions
Find the slope of the line that goes through the given points.74) (-2, -6), (-9, -17) 74)
A) 117
B) -117
C) 711
D) 2311
Use the given conditions to write an equation for the line in point-slope form.75) Slope = 4, passing through (-3, 7) 75)
A) x - 7 = 4(y + 3) B) y = 4x + 19 C) y + 7 = 4(x - 3) D) y - 7 = 4(x + 3)
Use the given conditions to write an equation for the line in slope-intercept form.
76) Slope = 23
, passing through (7, 3) 76)
A) y = 23
x + 7 B) y = 23
x - 53
C) y = mx - 53
D) y = 23
x + 53
77) Passing through (-8, -2) and (-5, -7) 77)
A) y = -53
x - 463
B) y + 2 = -53
(x + 8)
C) y = mx - 463
D) y = 53
x - 463
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Graph the line whose equation is given.78) y = 2x - 2 78)
A) B)
C) D)
Determine the slope and the y-intercept of the graph of the equation.79) 7x - 10y - 70 = 0 79)
A) m = 107
; (0, 10) B) m = 7; (0, 70) C) m = 710
; (0, -7) D) m = -710
; (0, 7)
Use the given conditions to write an equation for the line in the indicated form.80) Passing through (2, 3) and parallel to the line whose equation is y = -2x + 3 ;
point-slope form80)
A) y - 2 = -2(x - 3) B) y - 3 = -2(x - 2)C) y = 2x D) y - 3 = x - 2
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81) Passing through (5, 3) and perpendicular to the line whose equation is y = 2x + 7;point-slope form
81)
A) y - 3 =12
(x + 5) B) y - 3 = -12
(x - 5)
C) y - 5 =12
(x - 3) D) y = - 2x - 11
Find the average rate of change of the function from x1 to x2.
82) f(x) = -3x2 - x from x1 = 5 to x2 = 6 82)
A) -16
B) -34 C) -2 D) 12
Find and simplify the difference quotient of f, f(x + h) - f(x)h
, h 0, for the function.
83) f(x) = 4x2 83)
A) 4 B) 4(2x2 + 2xh + h2)h
C) 4(2x+h) D) 8h
+ x + 4h
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Topic #12: Transformations of Graphs
Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations of this graph to graph thegiven function.
84) h(x) = (x - 7)2 - 5 84)
A) B)
C) D)
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Use the graph of the function f, plotted with a solid line, to sketch the graph of the given function g.85) g(x) = -f(x - 1) + 2
y = f(x)
85)
A) B)
C) D)
Topic #13: Algebra of Functions, Function Composition, and Inverse Functions
Given functions f and g, perform the indicated operations.86) f(x) = 3 - 5x, g(x) = -8x + 5
Find f + g.86)
A) -5x B) 3x + 8 C) -8x + 3 D) -13x + 8
For the given functions f and g , find the indicated composition.87) f(x) = 3x + 9, g(x) = 5x - 1
Use the given zero to find the remaining zeros of the function.113) f(x) = x4 - 21x2 - 100; zero: -2i 113)
A) 2i, 5i, -5i B) 2i, 10, -10 C) 2i, 10i, -10i D) 2i, 5, -5
Divide using synthetic division.
114) x4 - 3x3 + x2 + 4x - 5x - 1
114)
A) x3 + 2x2 - x + 5 -2
x - 1B) x3 - 2x2 + x + 3 +
4x - 1
C) x3 - 2x2 + x + 5 +4
x - 1D) x3 - 2x2 - x + 3 -
2x - 1
Use the Leading Coefficient Test to determine the end behavior of the polynomial function.115) f(x) = 3x4 + 4x3 - 4x2 + 3x - 2 115)
A) rises to the left and rises to the right B) falls to the left and rises to the rightC) falls to the left and falls to the right D) rises to the left and falls to the right
116) f(x) = 2x3 + 5x2 + 5x + 5 116)A) falls to the left and rises to the right B) falls to the left and falls to the rightC) rises to the left and falls to the right D) rises to the left and rises to the right
Find the domain of the rational function.
117) g(x) = 2xx + 2
117)
A) {x|x -2} B) all real numbersC) {x|x 2} D) {x|x 0}
118) f(x) = x + 7x2 - 9
118)
A) {x|x -3, x 3, x -7} B) all real numbersC) {x|x -3, x 3} D) {x|x 0, x 9}
119) f(x) = x + 2x2 + 16x
119)
A) {x|x 0, x -16} B) {x|x -4, x 4, x -2}C) {x|x -4, x 4} D) all real numbers
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Find the vertical asymptotes of the rational function.
120) h(x) = 4x2(x + 2)(x - 6)
120)
A) x = -2, x = 6 B) x = -2, x = 6, x = -4C) x = 2, x = -6 D) x = -4
121) g(x) = x + 4x2 + 4
121)
A) x = -2, x = 2, x = -4 B) noneC) x = -2, x = -4 D) x = -2, x = 2