AnswersINMT3 Integrated Math 3 Sem 1 26-27Modeling with Quadratic Equations

Graphs of Rational Functions Answers

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

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Which graph represents the rational function ?

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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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The graph has a y-intercept at –2.
B
The graph has an x-intercept at –6.
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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.
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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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the time it takes the plane to travel without the tailwind
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the speed of the plane when there is no tailwind present
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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
6

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

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7

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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The greater the amount of acid added to the new substance, the more rapid the increase in acid concentration.
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The greater the amount of acid added to the new substance, the closer the acid concentration is to one-fifth.
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As more pure acid is added, the concentration of acid approaches 0.
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As more pure acid is added, the concentration of acid approaches 1.
8

Which graph represents the rational function ?

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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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at least one x-intercept
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at least one y-intercept
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an oblique asymptote
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a vertical asymptote
E
the domain of x
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