Determine whether the given statement makes sense or does not make sense, and explain your reasoning : "I’ve graphed a rational function that has two vertical asymptotes and two horizontal asymptotes."

Q: Find the Horizontal or Oblique Asymptote of a RationalFunction

A: Horizontal asymptotes assist in interpreting the behaviour of a graph as the input becomes very…

Q: Solve:(a) state the domain of the function, (b) identify all intercepts, (c) find any vertical or…

A: Explanation: Given that,  f(x)=-x(x-2)2   (a) Domain To find the domain of the function, we will set…

Q: I’ve graphed a rational function that has two vertical asymptotes and two horizontal…

A: The statement does not make the sense

Q: Graph all vertical and horizontal asymptotes of the rational function. - 6 f(x)=2x-7 -5-

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Q: The graph of a rational function cannot have both ahorizontal and an oblique asymptote. Explain why.

A: Query- The graph of a rational function cannot have both a horizontal and an oblique asymptote.…

Q: Do I have to factor to identify a rational function’s possible horizontal asymptote?

A:

Q: Follow the seven steps stategy to graph the rational function: f(x) =- 2/(x2 - x- 2)

A:

Q: It is possible to have a rational function whose graph has no y-intercept.Determine whether the…

A:

Q: Follow the seven steps stategy to graph the rational function: f(x) = 4x/(x2 - 1)

A: The steps are as below: Step 1) Factor numerator and denominator. Here, the numerator is 4x, so we…

Q: What are the horizontal asymptotes of f(x) = 4/e^x +1?

A: The horizontal asymptote of a function is a horizontal line such that the distance of function…

Q: Find the horizontal asymptote, if there is one,of the graph of the rational function f(x) =12x/(3x2…

A: Concept: Given:

Q: What are the vertical and horizontal asymptotes of the graph of y = 5-10x? Then graph the rational…

A: Vertical asymptote is the value for which the denominator is 0.

Q: What is the domain of a rational function?

A: Given: What is the domain of a rational function?

Q: If you are given the equation of a rational function, explain how to find the vertical asymptotes,…

A: If we have given the equation of a rational function f(x),the vertical asymptotes can be found by…

Q: Find the domain of the rational function.

A:

Q: Identify any vertical asymptotes of the function: 5x² f(x) = x² - 16 If there are none, briefly…

A: Horizontal asympototes  are y=5

Q: Determine whether the statement is true or false: "The graph of a rational function can never cross…

A: Known facts: There is a possibility  that the graph of rational function can cross the horizontal or…

Q: The graph of a rational function can never cross a vertical asymptote.Determine whether the…

A: It is known that the vertical asymptotes are obtained by solving the denominator. That is, the…

Q: Describe an asymptote, and explain when a rational function will have (a) a vertical asymptote and…

A: Asymptote

Q: Analyze the following graph of a rational function

A:

Q: Use the graph to find the horizontal asymptote of the rational function. y 10 5 -10 -5 10 -5

A: Horizontal asymptote

Q: To find the vertical asymptote of a graph of a rational function, you set the numerator equal to…

A: Given,         The vertical asymptote of a graph of a rational function.

Q: Write the equation of a rational function that has a hole at x=−5 and a vertical asymptote at x = 1.

A: We have given a rational function with Hole at x = -5 Vertical asymptote at x = 1 As if function…

Q: Find the horizontal asymptote, if there is one, of the graph of the rational function: f(x) =…

A: Consider the rule, for finding the horizontal asymptote of any given rational function. For any…

Q: Determine whether  the following statement is true or false, and explain why. Every rational…

A: Given statement, Every rational function has either a vertical or a horizontal asymptote - false

Q: Can the graph of a rational function have both a horizontal and an oblique asymptote? Explain.

A:

Q: Find the domain of a rational function

A: A rational function is defined as R(x)=P(x)Q(x) where the denominator  Q(x)≠0 So, if the denominator…

Q: (a) Under what circumstances does a rational function have a slant asymptote? (b) How do you…

A: (a)  The form the rational function is P(x)Q(x) where, P(x) is the numerator and the Q(x) is the…

Q: 2 x-5x+1 f(x) =- x-3

A: The given function f(x)=x2-5x+1x-3

Q: Find the vertical and horizontal asymptotes of the fiction f(x)= 1/x+1+2

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Q: Identify the rational function from the graph

A: Given that: Graph of r(x) as shown.

Q: Write a rational function with no vertical asymptotes and no holes. Explain.

A:

Q: Determine whether each of the following statements is true or false, and explain why Every rational…

A: Given Explain why Every rational function has either a vertical or a horizontal asymptote

Q: How do you find vertical asymptotes of rational functions?

A:

Q: Does the graph of every rational function have a vertical asymptote? Explain.

A: Does the graph of every rational function have a vertical asymptote? Explain.

Q: Sketch the graphs of the rational functions y = x2/x2 - 4

A: Given the function y = (x2)/(2x- 4). We need to plot the graph for the above function.

Q: Find the horizontal asymptote, if there is one,of the graph of the rational function h(x) =15x3/(3x2…

A: Solution:-  The given function is  h(x)=15x33x2+1

Q: (d) Plot additional solution points as needed to sketch the graph of the rational function.

A: Given function is as below :

Q: Write an example of a rational function which would have an end behavior asymptote which is…

A: Example of a rational function which would have an end behavior asymptote which is quadratic.…

Q: Sketch the graph the rational function, including all asymptotes. 4x 20) f(x) 20) (x + 1)(x - 2) ++…

A: The graph of the function is shown in the figure below with 3 asymptotes x=-1, x=2 and y=0

Q: Write an equation for a rational function with: Vertical asymptotes at x = -4 and x = -5

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Q: Write your own rational function that has a hole, but does not have a vertical asymptote. Make sure…

A: Given day of birth=28 We know that rational function is of the form p(x)/q(x)

Q: Identify all the asymptotes then graph the rational functions: f(x) = 4x2 2x -1

A: Asymptotes is x = 1/2

Q: Write the equations of the horizontal and vertical asymptotes, and find any holes in the graph, of…

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Q: Graph all vertical and horizontal asymptotes of the rational function. 4x-11 2x+9

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Q: Let f(x) = x – 3a c-3

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Q: Sketch the graphs of the rational functions y = x2 - 4/x2 - 3

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Q: Graph all vertical and horizontal asymptotes of the rational function. f(x) = x+2

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Q: State the vertical asymptote of the rational function. F(x)=(x-6)(x+6)/X^2-9

A:

Q: Explain the circumstances under which the graph of a rational function will have a hole.

A: A hole on a graph looks like a hollow circle.  It represents the fact that the function approaches…