AnswersLJISD-TX-Algebra II-4th 6WKSGraphs of Rational Functions

Graphs of Rational Functions Answers

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1
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The graph of has an oblique asymptote at y =

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A
x + 1.
B
4x + 3.
C
6x + 11.
D
62x + 34.
2
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A plane travels 2,000 kilometers at a speed of 900 kilometers per hour (kph) with no wind. When a tailwind is present, the plane’s speed increases by x kilometers per hour. The time it takes the plane to travel the same distance with the tailwind, t(x), is defined by the function . What is the meaning of the y-intercept for this function?

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A
the time it takes the plane to travel without the tailwind
B
the speed of the plane when there is no tailwind present
C
the minimum amount of time it takes the plane to travel 2,000 km
D
the time it takes the plane to travel when the speed is decreased by 900 kph
3

Which statements describe the key features of the graph of ? Check all that apply.The graph has a y-intercept at –2.The graph has an x-intercept at –6.The graph has a vertical asymptote at x = 3.The graph has a vertical asymptote at x = –3.The graph has a horizontal asymptote at y = 1.

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A
The graph has a y-intercept at –2.
B
The graph has an x-intercept at –6.
C
The graph has a vertical asymptote at x = 3.
D
The graph has a vertical asymptote at x = –3.
E
The graph has a horizontal asymptote at y = 1.
4

Which graph represents the rational function ?

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Option
Option A
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Option
Option B
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Option
Option C
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Option
Option D
5

Which function has a graph with a horizontal asymptote at y = 3, a vertical asymptote at x = 1, and an x-intercept at 2?

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Option
Option A
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Option
Option B
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Option
Option C
D
Option
Option D
6

What key features does f(x), shown in the graph, share with g(x), shown in the equation? Select three options.

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A
at least one x-intercept
B
at least one y-intercept
C
an oblique asymptote
D
a vertical asymptote
E
the domain of x
7

Which statements describe the end behavior of the graph of the function shown? Check all that apply.As x → ∞, y → 1.As x → ∞, y → ∞.As x → ∞, y → –∞.As x → –∞, y → 1.As x → –∞, y → ∞.As x → –∞, y → –∞.

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A
As x → ∞, y → 1.
B
As x → ∞, y → ∞.
C
As x → ∞, y → –∞.
D
As x → –∞, y → 1.
E
As x → –∞, y → ∞.
F
As x → –∞, y → –∞.
9

Consider the function .For which intervals is f(x) positive? Check all that apply.

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A
(–∞, –3)
B
(–3, –2)
C
(–2, 2)
D
(2, 3)
E
(∞, 3)
10

Question text not available

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A
The graph of f(x) does not pass through (0, 0); therefore, f(x) has no real zeros.
B
The graph of f(x) does not cross the x-axis; therefore, f(x) has no real zeros.
C
The graph of f(x) does not cross the y-axis; therefore, f(x) has no real zeros.
D
The graph of f(x) has one or more asymptotes; therefore, f(x) has no real zeros.
11

How would you describe the relationship between the real zero(s) and x-intercept(s) of the function

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A
When you set the function equal to zero, the solution is x = 1; therefore, the graph has an x-intercept of (1, 0).
B
When you set the function equal to zero, the solutions are x = 0 or x = 1; therefore, the graph has x-intercepts at (0, 0) and (1, 0).
C
When you substitute x = 0 into the function, there is no solution; therefore, the graph will not have any x-intercepts.
D
Since there are asymptotes at x = –3, x = –1, and x = 0, the graph has no x-intercepts and, therefore, no real zeros.
12

A plane travels 2,000 kilometers at a speed of 900 kilometers per hour (kph) with no wind. When a tailwind is present, the plane’s speed increases by x kilometers per hour. The time it takes the plane to travel the same distance with the tailwind, t(x), is defined by the function . What is the meaning of the y-intercept for this function?

Question illustration
A
the time it takes the plane to travel without the tailwind
B
the speed of the plane when there is no tailwind present
C
the minimum amount of time it takes the plane to travel 2,000 km
D
the time it takes the plane to travel when the speed is decreased by 900 kph
13

Identify the graph of a rational function that is decreasing on the interval (–5, 5).

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
14

Question text not available

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A
f(x) has one real zero at –2 because the graph of the function has an intercept at (0, –2).
B
f(x) has two real zeros at –4 and –2 because the graph of the function has intercepts at (–4, 0) and (0, –2).
C
f(x) has no real zeros because the graph of the function does not pass through (0, 0).
D
f(x) has one real zero at –4 because the graph of the function has an intercept at (–4, 0).
15

A pure acid measuring x liters is added to 300 liters of a 20% acidic solution. The concentration of acid, f(x), in the new substance is equal to the liters of pure acid divided by the liters of the new substance, or . Which statement describes the meaning of the horizontal asymptote?

Question illustration
A
The greater the amount of acid added to the new substance, the more rapid the increase in acid concentration.
B
The greater the amount of acid added to the new substance, the closer the acid concentration is to one-fifth.
C
As more pure acid is added, the concentration of acid approaches 0.
D
As more pure acid is added, the concentration of acid approaches 1.
16

A pure acid measuring x liters is added to 300 liters of a 20% acidic solution. The concentration of acid, f(x), in the new substance is equal to the liters of pure acid divided by the liters of the new substance, or . Which statement describes the meaning of the horizontal asymptote?

Question illustration
A
The greater the amount of acid added to the new substance, the more rapid the increase in acid concentration.
B
The greater the amount of acid added to the new substance, the closer the acid concentration is to one-fifth.
C
As more pure acid is added, the concentration of acid approaches 0.
D
As more pure acid is added, the concentration of acid approaches 1.
17

Which function has a graph with a horizontal asymptote at y = 3, a vertical asymptote at x = 1, and an x-intercept at 2?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
18

Question text not available

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Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
19

Which graph represents the rational function ?

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Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
20

If the graph of has an oblique asymptote at y = 3x + k, what is the value of k?

Answer not available
21

Which graph represents the rational function ?

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Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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