Download Rationals Multiple Choice Post-Test

Name: _____________________________
Class: _____________ Date: __________
Rationals Multiple Choice Post-Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1 Which family of functions does y =
A Trigonometric
B Logarithmic
____
____
4
belong to?
x2
C Exponential
D Rational
2 Which of the following functions is not rational?
1
x
x−4
f(x) =
x+8
3x
x+5
x2 − 1
f(x) = 2
x + 2x + 1
A f(x) =
C f(x) =
B
D
3 Simplify the expression and state the excluded values:
A −p + 8; p ≠ −4
B p − 8; p ≠ −4
p 2 − 4p − 32
p+4
C −p − 8; p ≠ 4
D p + 8; p ≠ 4
.
____
4 Multiply. State the excluded values:
A
B
____
z+3
z+2
z+3
5 Simplify:
A
B
____
z 2 + 2z
, z ≠ −1, 0, − 3
a+8
+
7
2
a − 64
z+1
⋅
z 2 + 3z + 2
z 2 + 3z
C
, z ≠ −1, − 3
7
z2
D
z+2
z+3
.
, z ≠ −1, − 3
z 2 + 2z
z+3
, z ≠ −1, 0, − 3
.
7a − 49
(a − 8)(a + 8)
14
2
a + a − 56
6 Given the graph of the function f(x) =
C
14
(a − 8)(a + 8)
D
7a + 63
(a − 8)(a + 8)
1
. Which of the following represents the behavior of the function
x2
as x approaches negative infinity?
A approaches negative infinity
B approaches zero
Algebra II Rationals Post-Test
C approaches positive infinity
D approaches one
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____
____
7 Describe the vertical asymptote(s) and hole(s) for the graph of y =
(x − 5)(x − 2)
(x − 2)(x + 4)
.
A asymptote: x = –4 and hole: x = 2
C asymptote: x = –5 and hole: x = –4
B
D asymptote: x = 4 and hole: x = –2
asymptotes: x = –4 and x = 2
8 If R is the total resistance for a parallel circuit with two resistors of resistances r 1 and r 2 , then
1
R
1
=
r1
+
1
r2
. Find the resistance r 1 if the total resistance R is 20 ohms and r 2 is 75 ohms. Round your
answer to the nearest ohm if necessary.
____
A 16 ohms
C 27 ohms
B
D 102 ohms
1405 ohms
9 Solve the equation for x:
A −
B
____
−2
x+4
=
4
x+3
.
13
6
D
−11
10 Solve the equation for w:
3
14
11
6
8
3
11
−
3
C −
5
6w
+
1
w
= −4.
11
24
31
−
24
A −
C −
B
D
Algebra II Rationals Post-Test
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____
11 A group of high school students are volunteering for Habitat for Humanity during their summer break.
They are putting the finishing touches on a house they built. Working alone, Kendra can paint a certain
room in 7 hours. Joe can paint the same room in 6 hours. Write an equation that can be used to find how
long it will take them working together to paint the room. How many hours will it take them to paint the
room? If necessary, round your answer to the nearest tenth.
7 6
1 1
1
A
+
= 1; 13 hours
C
+
= ; 6.5 hours
x x
7 6
x
x x
x x
+
= 1; 3.2 hours
+
= 1; 6.5 hours
B
D
7 6
6 7
____
12 Sketch the asymptotes and graph the function.
y =
x 2 − 7x + 12
x2 − 1
A
C
B
D
Algebra II Rationals Post-Test
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____
13 State the domain of the function y =
A
B
____
B
____
____
x || x ≠ 9,x ≠ 7
x || x ≠ −9,x ≠ − 7
14 Simplify the following expression:
A
(x + 6)(x + 2)(x + 8)
.
(x + 9)(x + 7)
(x + 2)(x + 5)
x+4
(x + 2)(x + 4)
C
D
x+2
x−1
÷
x+4
2
x + 4x − 5
, x ≠ − 5, − 4
C
, x ≠ 1, − 5
D
(x − 1) 2 (x + 5)
x || x ≠ −6,x ≠ −2,x ≠ −8
x || x ∈ ℜ
(x + 2)(x + 4)
, x ≠ 1, − 5, − 4
(x − 1) 2 (x + 5)
(x + 2)(x + 5)
;x ≠ 1,−4,−5
x+4
15 Determine the horizontal asymptote of the function. y =
A
y=3
B
y=−
C y=
1
3
.
6x 2 + 1
.
2x 2 − 3
1
3
D y = −3
16 Which function does not have a horizontal asymptote.
A g(x) =
x−6
x2 + 2
x2
g(x) =
−3x 2 + 1
C g(x) =
x−9
x+3
B
D g(x) =
x3 − 2
6x 2 − 5
Algebra II Rationals Post-Test
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____
17 Reduce the fraction to lowest terms:
8x 2 + 4x
.
2x
C 2x 2 + 1
A 2x + 1
B
____
4x 2 + 2
18 Solve the equation
D 4x + 2
1
1
4
+
= 2
for x.
x+2 x−2 x −4
A x=1
B x=4
____
19 Find the x-intercept of the function: h(x) =
A (-1,0)
B (1,0)
Algebra II Rationals Post-Test
C No solution
D x=2
x 2 − 2x + 1
.
x2 − 1
C (0,1)
D there is no x-intercept
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____
20 Solve for y, then graph the function.
xy + 16 = 0
____
A
C
B
D
21 Describe the vertical asymptote(s) and hole(s) for the graph of y =
(x − 5)(x − 2)
(x − 2)(x + 4)
.
A asymptote: x = - 4 and hole: x = 2
C asymptote: x = - 5 and hole: x = -4
B
D asymptote: x = 4 and hole: x = -2
asymptotes: x = - 4 and x = -2
Algebra II Rationals Post-Test
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____
22
Which equation best represents the graph?
____
A y=
(x − 2)
(x − 4)
C y=
(x + 4)
(x − 2)
B
(x + 2)
(x + 4)
D y=
(x + 2)
(x − 4)
y=
23 Describe the holes for the graph of the rational function y =
(x − 2)
.
(x − 2)(x + 5)
A Hole: x = –2
C Hole: x = – 5
B
D Hole: x = 5
Hole: x = 2
Algebra II Rationals Post-Test
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____
24 What are the x and y-intercepts of the rational function R(x) =
A x-intecepts: (4, 0) and (-3, 0)
C x-intecepts: (4, 0) and (-3, 0)
y-intercept: (0, –2)
B
____
____
x-intecepts: (-4, 0) and (3, 0)
1
y-intercept: (0, 6 )
x 2 − x − 12
?
x+6
y-intercept: (0, 2)
D x-intecepts: (-4, 0) and (3, 0)
y-intercept: (0, -2)
25 Find any points of discontinuity for the rational function: y =
(x + 6)(x + 2)(x + 8)
(x + 9)(x + 7)
A
x =6 x =2, x = 8
C
B
x = 9, x = 7
D x = -6, x = -2, x = -8
.
x = -9, x = -7
26 What are the vertical and horizontal asymptotes of the rational function?
y =
A Vertical Asymptotes: x = 2
Horizontal Asymptotes y = 3
B
Vertical Asymptotes: x = 2
Horizontal Asymptotes y = –3
Algebra II Rationals Post-Test
1
x+2
−3
C Vertical Asymptotes: x = –2
Horizontal Asymptotes y = –3
D Vertical Asymptotes: x = –2
Horizontal Asymptotes y = 3
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____
27 Determine the end behavior of the function.
f(x) =
____
(2x − 4)
(2x 2 − 1)
A As the x-values approach negative
infinity, the graph approaches the
horizontal asymptote from below. As
the x-values approach positive
infinity, the graph approaches the
horizontal asymptote from above.
C As the x-values approach negative
infinity, the graph approaches the
vertical asymptote from below. As the
x-values approach positive infinity,
the graph approaches the horizontal
asymptote from above.
B
D As the x-values approach negative
infinity, the graph approaches the
horizontal asymptote from above. As
the x-values approach positive
infinity, the graph approaches the
horizontal asymptote from above.
As the x-values approach negative
infinity, the graph approaches the
horizontal asymptote from below. As
the x-values approach positive
infinity, the graph approaches the
horizontal asymptote from below.
28 Determine the horizontal asymptotes of the function: g(x) =
x2 + 1
.
x−2
A Horizontal asymptote: y = –1
C Horizontal asymptote: y = 1/2
B
D There is no horizontal asymptote
Horizontal asymptote: y = 2
Algebra II Rationals Post-Test
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____
29 Simplify the following rational expression, state any excluded values.
2x
4x
− 2
x − x − 2 x − 3x + 2
2
____
A
−2x 2 − 6x
,x ≠ ±1,x ≠ 2
(x − 2)(x + 1)(x − 1)
C
−2x 2 + 2x
,x ≠ ±1,x ≠ 2
(x − 2)(x + 1)(x − 1)
B
6x 2 + 2x
,x ≠ ±1,x ≠ 2
(x − 2)(x + 1)(x − 1)
D
6x 2 − 6x
,x ≠ ±1,x ≠ 2
(x − 2)(x + 1)(x − 1)
30 Simplify the following rational expression, state any excluded values.
4
7
−
x −9 x+3
2
A
B
____
7x + 25
,x ≠ ±3
x2 − 9
7x − 17
,x ≠ ±3
x2 − 9
C
D
−7x + 25
,x ≠ ±3
x2 − 9
−7x − 17
,x ≠ ±3
x2 − 9
31 Simplify the following rational expression, state any excluded values..
x 3 − 5x 2 + 6x x 2 + 3x + 2
• 2
x2 − 4
x − 2x − 3
____
x(x − 2)
,x ≠ ±2,x ≠ 3,x ≠ −1
(x + 2)
A 1
C
B
D x, no restrictions
x, x ≠ ±2,x ≠ 3,x ≠ −1
32 Simplify the following rational expression, state any excluded values..
x 2 − 5x + 6 x 2 + 3x − 10
÷
x3
4x 2
A
B
8(x − 3)
' x ≠ −5,x ≠ 0,x ≠ 2
3(x + 5)
(x 2 − 5x + 6)(x 2 + 3x − 10)
Algebra II Rationals Post-Test
4x
5
,x ≠ 0
C
4(x − 3)(x + 2)
' x ≠ −5,x ≠ 0,x ≠ 2
x(x + 5)(x − 2)
D
4(x − 3)
' x ≠ −5,x ≠ 0,x ≠ 2
x(x + 5)
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____
1
x
33 Write the equation of the parent function f(x) = , after a translation of 3 to the left and 5 down.
A
B
____
1
−5
x+3
1
f(x) =
+5
x+3
f(x) =
C
D
1
−5
x−3
1
f(x) =
+5
x−3
f(x) =
1
x
34 The graph below is a transformation of the parent function f(x) = . Write the equation of the graph.
A
B
1
−5
x−1
1
f(x) =
−5
x+1
f(x) =
Algebra II Rationals Post-Test
C
D
−1
−5
x−1
−1
f(x) =
−5
x+1
f(x) =
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