1). Answer the questions below, given the three rational functions in the chart. The function y = f(x) shown y = h(x) shown B(x) =- x-3 a) State in words the transformation(s) which map the graph of g(x) onto the graph of f(x). b) Is it possible to use transformations to map the graph of f(x) onto the graph of h(x)? State YES or NO: Justify your answer in words: c) State two key features which are similar to ALL three graphs. Be precise in the way you describe similarity. i.) ii.) d) State one key feature is not present in all three graphs. precise in the way you describe this difference. i.)

Q: Consider finding a rational function p(x) = (a + bx)/(1 + cx) that satisfies p(x,) = yi i = 1,2,3…

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Q: x + a f(x) = x +b

A: Introduction  A rational function is any function which can be defined by a rational fraction, Which…

Q: 1. Explain why both f(x)= x³+ 1 and g(x) tions. x3+1 are rational func-

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Q: Pg 487 Question #6 Give the equations of any (a) vertical and (b) horizontal asymptotes for the…

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Q: Find the domain of the rational function. x-8 f (x) = x+2 Enter your answer in interval notation. To…

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Q: 3. Sketch a possible graph of a rational function, y = fAx), that has all the following properties…

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Q: 18. Determine the domain restrictions for the rational function below. y= 6 2+5 Ox-5 Oz #5 02-6 Oz‡6

A: domain means which x value we can put in equation so function is define y = 6/(x+5) function is only…

Q: Use transformations of f(x) = 1/x or f(x) = 1/x2 to graph the rational function: g(x) =1/(x-3)2 + 1

A: This means f(x) will move 3 units to right and 1 unit up.

Q: Example 3.6.2 Sketch the graph of y = f(x) = (2) Answer: A. The function is not defined at 3, so the…

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Q: 2. Determine the equation for the graph of the following rational function. (0.5, -0.16)

A: Rational function: Rational function is of the form p(x)q(x), where px and qx are polynomials. The…

Q: A rational function f(x) has one vertical asymptote x= 2, and one horizontal asymptote, y=-3 and the…

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Q: What is the equation for the horizontal asymptote of the rational functional graph? 1) y=2 2)Y=3…

A: The domain of the given function is, D=x|x≠2 The rage of the function is,

Q: 10 Identify the vertical asymptotes of f(x) = x2 - 7x - 30 Ox= = 10 and x = 3 Ox = 10 and x = -3 Ox=…

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Q: -2 For the function H(x) = 4: (a) graph the rational function using transformations, (b) use the…

A: We first graph the function using a graphing calculator Option D matches this graph.

Q: 5x-2 Let the rational function f be defined as R(x) 3x-1

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Q: a)Prove that 3d − c = 2. b)If the vertical asymptote of the above rational function is the line x =…

A: We have to- prove that 3d − c = 2,   determine the value of d,   determine the value of c, and…

Q: How is the graph of g(x)=-(2x) related to the graph of f(x) = x? A The graph of g(x) is a horizontal…

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Q: 1 The vertical asymptotes of (3) = %3D are O a) x= 0 and x= 1 Ob) x= 1and x= 2 Oc) x= 1 and x= -1 O…

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Q: 13. Sketch a graph of a rational function that satisfies the following conditions Text f(0) = 0,…

A: 1. If f''(x) > 0 , f(x) is concave upward.   2. If f''(x) > 0 , f(x) is concave downward.   3.…

Q: -3 -2 -1 3 12 For the above rational function f( x ) = 2x2 identify the interval on which f is…

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Q: The graph of a rational function, g(z), is shown here

A: Given that: Graph of f(x)

Q: What is the domain of the parent rational function f (x) = =? Choose all that apply O -00,0) U (0,…

A: Find domain.

Q: 15. Graph the rational function )- T- a.

A: Check asymptote, intercept,extrema then make graph

Q: 5. Sketch the graph of the following rational function. 2x – 1 f(x) x² + 2x – 3 Part A: y…

A: In the question it is asked to draw the graph and mark points in it.

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: 8. Graph the following rational function. Show ALL steps CLEARLY. (C__R_ 2x – 4 f(x) = x+3 b. State…

A: Given the function is  The graph of function is

Q: 22. Sketch the graph of each of the following rational functions. Ex following. i. the equations of…

A: We have to use properties of rational function to solve the problem

Q: 1. Write an equation of a rational function that satisfies ALL of the given the given conditions…

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Q: Find a formula for the rational function f(x) that satisfies the following conditions. Simplify the…

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Q: 6. Read each set of conditions. State the equation of a rational function ax + b of the form f(x)…

A: Dear learner, As per our guidelines, we can provide the solution for first one only. Kindly post…

Q: 8. Graph the following rational function. Show ALL steps CLEARLY. (C_ R 2x – 4 f(x) = x + 3

A: Here we have to graph the given function.  We have,

Q: Use transformations of f(x) = 1/x or f(x) = 1/x2 to graph the rational function: g(x) =1/(x-3)2 + 2

A: Given information: fx=1xfx=1x2gx=1x-32+2

Q: Use transformations of the graph of y = 1/x to graph the rational function r(x) = X - 1

A: Domain set of all input values where f defined Range Set of all output values

Q: Graph the following rational function using transformations. 1 F(x) = -6+ .... Select the correct…

A: Given that: F(x)=-6+1x

Q: 3 The rational function r (x)= 1 is a transformation of its parent - x- 2 function f (z)= Which of…

A: f(x-a).....shift by a units right af(x)......vertical stretch by a -f(x).......Reflection across x…

Q: Determine a possible formula of least degree for the rational function g(x) whose graph is shown…

A: Given query is to find the function for the graph.

Q: Consider the function 6 x +350 - xi - 500 f(x) = %3D 14 x - 180 - xi+ 1000 - x The graph of y = f(x)…

A: Given

Q: Suppose the functions f and ĝ are defined by y = f(x) = 5*+1 –1 and y = g(x) = 5* - respectively.…

A: Given,

Q: Consider the following rational function. 6 f(x) : %3D x- 7 Step 3 of 3: Identify four ordered pairs…

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Q: 1) State the vertical asymptotes of f(x)= a. x=6₂x=-2 b. x=6, x=2 1 x² - 4x-12 c. d. x=-6, x=-2…

A: Given:         fx=1x2-4x-12 Vertical Asymptote:     For rational functions,the vertical asymptotes…

Q: 3. Sketch the graph of the following rational function. 10x? + 11x – 6 g(x): 8x Part A: y…

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Q: Use transformations of the graph of y = 1/x to graph the rational function, and state the domain and…

A: Given information: The function is r(x)=1x-1. Graph: Suppose the parent function is f(x)=1x. The new…

Q: Use transformations of f(x) = 1/x or f(x) =1/x2 to graph the rational function : h(x) = [1/(x - 1)]…

A: hx=1x-1+3 The graph of hx=1x-1+3 is obtained by horizontally shifting the graph of fx=1x to the…

Q: 8 R -5 -4 -3 -2 -1 3+ For the above rational function f( x ) = lowest = middle = highest = 12 %3D…

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Q: 8) Graph the rational function R(x) = using transformations. Determine the (x-3)2 domain, range,…

A: We will use transformations on f(x)=1x2 to sketch the rational function 2(x-3)2. So, first we will…

Q: Use transformations of f(x) = 1/x or f(x) =1/x2 to graph the rational function : g(x) = [1/(x + 2)2]…

A: fx=1x2 The graph is,

Q: 2+1 22-4. Sketch the graph of the rational function r(z)=

A: Here in this question we have to plot the graph of given rational function.

Q: 13. Sketch a graph of a rational function that satisfies the following conditions f(0) = 0, f(-4) =…

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Q: Sketch the graphs of the rational functions y = x4 - 1/x2

A: Given:         y=x4−1x2