EXAMPLE 2 Using Transformations to Graph Rational Functions Graph each rational function, and state the domain and range. 2 3x + 5 (a) r(x) (b) s(x) %3D x - 3 x + 2

Q: EXAMPLE 8 Graphing a Rational Function 4x Graph f(x) x - 4

A: we have to graph the rational function f(x)=4xx2-4

Q: EXAMPLE 1 Investigating the Behavior of a Rational Function The graph of f(x) 1 is given. Complete…

A: The given rational function is f(x)=1x2

Q: EXAMPLE 7 Graphing a Rational Function 5x + 21 Graph r(x) and state the domain and range. x² + 10x +…

A: Given rational function is: rx=NxDx=5x+21x2+10x+25

Q: Among all deaths from a particular disease, the percentage that is smoking related 21–39 cigarettes…

A: The rational function that models the percentage of smoking-related deaths among all deaths from a…

Q: 2. How do the asymptote and intercept of the given function compare to the asymptote and intercept…

A: Given f(x)=5x, g(x)=5x+3

Q: Sketch the graph of the rational function below, including all asymptotes.  Make sure that you…

A: In the question we have to find asymptotes of the given function.

Q: snip

A: we have to graph the given rational function. R(x)=1(x-2)2+1

Q: x3-8 ] Find the asymptotes of the function f (x): x² -4

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Q: 6x-2x+1 Find the horizontal asymptotes of the function of f(x)= 3x-2x-2

A: Given function is: f(x) = (6x2 - 2x + 1)/(3x3 - 2x2 - 2) The corresponding graph is:

Q: Find a rational function that might have the given graph. (More than one answer might be possible.)

A: According to the given figure, x - intercept is x = 0. Vertical asymptotes are x = 2, x = -2…

Q: Identify the rational function whose graph is given below. Note that the function has a x-intercept…

A: Given that the function has x intercept at x = –3 and y intercept of y = 3/2.Also, from the graph it…

Q: Finding Horizontal Asymptotes Example 6 - 2x+5x-9 (x) = x+1

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Q: Write an equation for the function graphed below. It is a rational function with: Horizontal…

A: The given graph:         The given details: It is a rational function with, Horizontal asymptote:…

Q: Use transformations of the graph of y = 1/x to graph the rational function, as in Example 2. 4 s(x)…

A: Parent function  F(x) = 1/x

Q: Finding Horizontal Asymptotes Example 6 - 2x+5x-9 (x)= %3D If x+1

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Q: Write an equation for a rational function graphed below. Notice that the green dashed lines are…

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Q: Graph the rational functions in Exercise. Include the graphsand equations of the asymptotes.

A: Given: Graph the rational functions in Exercise. Include the graphs and equations of the…

Q: Question Identify the rational function whose graph is given below. The yintercept is (0,-). 4- 3 2…

A: Ans is

Q: 6. Based on data from the U.S. Department of Agriculture, the average number of acres per farm x…

A: Given model. A(x)=(2078x-94458)/(13x-2164)

Q: How many horizontal asymptotes can the graph of a given rational function have? Give reasons for…

A: A graph can have at most two horizontal asymptotes. We get horizontal asymptotes when x approaches…

Q: Verify that the function ƒ as given is symmetric about the origin by showing that ƒ(-x) = -ƒ(x).

A: Given that  f(x)=10x3x2-1

Q: 11. [5 points]: Graph the rational function (5x-2)(x-1)2(x+2)(x+4) 7x(x+2)(x-3)(x-5)2 r (x)…

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Q: 9. True or False The graph of a rational function may intersect a horizontal asymptote.

A: GIVEN The graph of a rational function may intersect a horizontal asymptote. we need to verify true…

Q: 16. What is the vertical asymptote of the function f(x) = ? %3D x2-9 A. x = -3 & x 3 B. X 0 C. x 3…

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Q: Use transformations of the graph of y = 1/x to graph the rational function, as in Example 2. 4х - 17…

A: r(x)=4x-17x-4r(x)=4x-16-1x-4r(x)=4(x-4)-1x-4r(x)=4(x-4)(x-4)-1(x-4)r(x)=4-1(x-4)r(x)=4-f(x-4)r(x)=-f…

Q: Graphing a rational function, Indicate all asymtopes,holes and crossing of the x-axis r(x)=…

A: Given rational function is r(x)=4x7-11x6+x5-8x+113x5+x2-1              (1) if we put x=0 in the (1),…

Q: EXAMPLE 6 Graphing a Rational Function x² – 4 2x2 + 2x Graph the rational function r(x) and state…

A: The rational function is input into a graphing utility and proper limits are set up. The horizontal…

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

A: No, Not every rational function has a vertical asymptotes.  If a function have domain all real…

Q: EXAMPLE 4 Finding Vertical Asymptotes Find the vertical asymptotes, if any, of the graph of each…

A: (a) Given function is: Fx=x+3x-1 The denominator becomes zero if: x - 1 = 0 x = 1 Therefore the line…

Q: In Problem,find a rational function that might have the given graph.(More than one answer might be…

A: Consider the expression for the rational function, as f(x)=a(...) (...)(...)(...), where a is the…

Q: 2x-1 Graph the rational function f(x)= -2x+4 To graph the function, draw the horizontal and vertical…

A:

Q: Which is not true about the graph of a rational function? A. It is not continuous. B. It is made up…

A: Which is not true about the graph of a rational function?A. It is not continuous.B. It is made up of…

Q: The graph of a rational function is shown below. Write the equation that rep- resents this function.…

A:

Q: The graph of the rational function f(r) is shown below. Using the graph, determine which of the…

A: given graph

Q: Consider the rational function f given below. 2-x- 42 f(x) = %3D X +x- 30 Identify any vertical…

A: To find the vertical asymptote

Q: Use transformations of the graph of y = 1/x to graph the rational function, as in Example 2. x +5 x…

A:

Q: Example: - The domain of f(x) =x and g(x) = x- 1 the domain of the rational function (g/f) (x) = is…

A:

Q: EXAMPLE 5 Graphing a Rational Function 2x + 7x - 4 Graph r(x) and state the domain and range. x? + x…

A: Given: rx=2x2+7x-4x2+x-2 To Find: Domain and Range

Q: 2. Determine the domain and range of the rational function graphed below 6- 5- 4 3 21 C. -9 -8 -7 -2…

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: -7x+3 Graph the rational function f(x) -4x-6 To graph the function, draw the horizontal and vertical…

A:

Q: Example: - The domain of f(x) = x and g(x) = x- 1 the domain of x2 the rational function (g/f) (x) =…

A: (g/f) (x) = x2x-1        [x≥1]Clearly,  gf(x) is defined for all x∈R except x=1

Q: The graph of the rational function f(x) is shown below. Using the graph, determine which of the…

A: The graph tends to ∞ as the value of x tends to 3 from the left side. The graph tends to -∞ as the…

Q: (3x-6)(x-4) x(r-4)

A: Domain of  3x-6x :  Solution:  x<0  or   x>0  Interval Notation: -∞ , 0∪0, ∞ Range of 3x-6x:…

Q: EXAMPLE 3 Asymptotes of a Rational Function 2x2 - 4x + 5 Graph r(x) and state the domain and range.…

A: r(x)=2x2-4x+5x2-2x+1

Q: x° - 125 Follow the steps for graphing a rational function to graph the function H(x) = x² - 64

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Q: 140x f(x)%3D 100- X models the cost, in millions of dollars, to inoculate x% of the population…

A: Given Data: Function: fx=140x100-x   For f70, Substitute 70 for x in the function.…

Q: Use transformations of the graph of y = 1/x to graph the rational function, as in Example 2. 1 r(x)…

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Q: The graph of the rational function f(x) is shown below. Using the graph, determine which of the…

A: topic - limits and sketch of a function  i have marked tick which are correct and cross which does…

Q: x-2 Graph the rational function f(x) = X-1

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Q: Finding Horizontal Asymptote Example 5 6x - 3x +5 g(x)= 5x +7x-9 If

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