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

Graphs of Rational Functions Answers

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Which graph represents the rational function ?

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Option D
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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.
3

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

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Option D
4

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?

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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.
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 A
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Option D
7

At which values of x does the graph of have a vertical asymptote? Check all that apply.–4–1124

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A
–4
B
–1
C
1
D
2
E
4
8

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.
9

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
10

Question text not available

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Option A
B
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Option B
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Option C
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Option D
11

Which statements describe the end behavior of the graph of the function shown? Check all that apply.

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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 → –∞.
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

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
14

Question text not available

Question illustration
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.
15

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
16

At which values of x does the graph of have a vertical asymptote? Check all that apply.

Question illustration
A
–4
B
–1
C
1
D
2
E
4
17

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
18

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.

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