a. Graph the functions f(x) = 3/(x - 1) and g(r) = 2/r + 1) together to identify the values of x for which 3 2 x + 1 b. Confirm your findings in part (a) algebraically.

Q: Use the graph of f(x) = 2x to obtain the graph of g(x) = 2x + 1.

A: g(x)= 2x + 1 = f(x)+1 This means f(x) will move 1 unit up to make g(x). Graph of f(x) is:

Q: Use the graph of f(x) = lxl to obtain the graph of g(x) = lxl + 3.

A: g(x)=|x|+3= f(x)+3 So, this means f(x) shifted 3 units up to make g(x).

Q: True or false: The graph of the reciprocal function f(x) =1/x has a break and is composed of two…

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Q: Analyze the graph of f (x) = ln(x2 + 2x + 3).

A: The given function is f(x)=lnx2+2x+3

Q: For what values of x does the graph of f(x)=2x^3+15x^2−36x−5 have a horizontal tangent line?

A:

Q: Given the function f, find the slope of the line tangent to the graph of f -1 at the specified point…

A: Given, The function is f(x)=-x2+8 and the point on the graph of f-1(x) is (7,1).

Q: Please I want solution of question 4 with step by step. Many Thanks

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Q: Consider the functions :  f(x)=√x and g(x)=x-1 Solve for- (f°g) (x)

A: Given:

Q: Express f(x)= x2 +4x + 1 in standard form. Find thevertex of the graph and the maximum or minimum…

A: We will complete the square for f(x) Answer(a): Standard form: f(x)= (x+2)2 -3

Q: 4. If f(x) = ax³ + bx², determine a and b so that the graph of f will have a point of inflection at…

A: If fx=ax3+bx2, then to determine a and b so that the graph of f will have a point of inflection at…

Q: Given the function​ f, find the slope of the line tangent to the graph of f-1 at the specified point…

A: Obtain the inverse of the given function as follows:

Q: Let: f(x)=x² +, f'(x) =2x-- 21 f"x)=2+ 1. Find x- and y- intercepts of the graph of f, if it has…

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Q: 11) Find the point of inflection of the graph of the function. f(x) = xVx – 27 %3D

A:

Q: 22. Find the maximum or the minimum value of f(x)=-2x² –10x+5. SLO 11

A: To find the maximum and minimum values of the function

Q: Consider f(x)=ax3+bx2+cx+d Under what conditions on a,b,c,and d does the graph of a cubic function…

A:

Q: 5- For the function f(x)=x³/3(x²-3) – 3/2, determine: a- The domain. b- The x and y intercepts. c-…

A: Given problem:-

Q: Find f^-1 (x), if it exists, and graph both f(x) and f^-1 (x).  f(x)= 2x^3 -3

A: Topic  =Functions

Q: Does y = e9-x* – 2 exist? What is the domain & range of the function if it does exist?

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Q: Use the graph of f(x) = 3x to obtain the graph of g(x) = 3x+1.

A: To determine: Graph of g(x)=3x+1 using the graph of f(x)=3x

Q: Given that f(-5)=-5  and f'(-5)=-10 , find an equation for the tangent line to the graph y=f(x) of…

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Q: Use the graph of f(x) = lxl to obtain the graph of g(x) = lxl - 4.

A: Given function is fx=x. To transform gx=x-4 from the graph of fx=x. Since the graph of g has -4,…

Q: Find the absolute maximum and absolute minimum values of the function f(x) = -x3 + 12x + 6, over the…

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Q: Two key points on the graph of g(x)=8^x are (1, _) and (0,_)

A: Given the function  g(x) = 8x we need to find it's two key points with given information. Now let (1…

Q: Find the values of a and b such that (-1, 2) is a point of inflection on the graph of f (x) = ax-…

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Q: Does the function g(x)=2-x  approach a certain real number as the value of x increasing positively?…

A: Given - g(x) = 2-x To find - Does the function g(x) approach a certain real number as the value of x…

Q: 3. For what value of x does the graph of f (x) = e* – 2x have a horizontal tange

A: Solve the following

Q: 2. Suppose the function f is defined as f(x): vertical asymptote(s) of f.( 6x²-8 (x-2)(x+4)' .Write…

A: As we know that; To calculate the vertical asymptotes, equate the denominator to zero and solve for…

Q: In certain conditions, the atmospheric pressure (p) in the height (h) is given by p=29e-0.000034h.…

A: It is given that the atmospheric pressure in the height is given by the function…

Q: Find the absolute maximum value of the function f(x) = 5(x - e

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Q: 11. Sketch the graph of the following function. f(x)= x³ - 6x² - 9x [1]x- and y-intercepts

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Q: given the function f(x)=axln(x+b), where function is decreasing at x=1-b?

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Q: Consider the function: f(x)= 4x^2-9/-x^2+x+6. Find the equation of the vertical asymptote(s)(if…

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Q: 11. Sketch the graph of the following function. f(x)= x³6x² - 9x [1]x- and y-intercepts

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Q: Find the point on the graph of f(x)=4−x2 that is closest to the point (0,1).

A: To find the point on the graph of fx=4-x2 that is closest to the point (0,1)

Q: Find the function f(x) given that f ′ (x) = e x + x and the graph of f passes through the point (0,…

A: Given: f'x=ex+x & Px,y=0,3   As we know that; The Power rule: ∫xndx=xn+1n+1+C And…

Q: Consider the function f(x)=(x+1)(x–1)2, At what value of x will the graph of f cross the y-axis?…

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Q: For which values of x does the graph of  f(x) = 8x3 - 12x2 - 24 have a horizontal tangent? Enter…

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Q: Find the point on the graph of f (x) = 4 − x2 that is closest to the point (0 , 1).

A: Given function f(x)=4-x2 To find the point on the graph of f which is closest to the point (0,1)

Q: 5) The graph of the function f(x) = 4-x has an inflection point at

A: Given: fx=x4-x We know that for any function, inflection point are points where second derivative of…

Q: For the function f(x)=x3-3x what is the local maximum and where does it occur? what is the local…

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Q: Find the values of x for all points on the graph of f(x)=x3-2x2+5x-16x at which the slope of the…

A: The given function is

Q: The graph of function f(x) = x – 9x² + 7x is concave upwards on (-0, c0) O (-∞, 3) O (3, 0) O None

A: Given function is  f(x)= x^3 - 9x^2 + 7x

Q: Determine the vertex of the function f(x)= lx-1l -1 How do I solve this?

A:

Q: 2. Find the value of k if the graph of k f(x) = 3x? has a point of inflection at x = -1.

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Q: 18. When is the function, f (x)=: 4 -3x? -3+ below the horizontal asymptote? x-1 5-4x-x2

A: It is given that the function fx=4x-1-3+-3x25-4x-x2. 5-4x-x2=5-5x+x-x2               =51-x+x1-x…

Q: Shasta was working at differentiating a function p(x) and they found that p'(0) = In Unfortunately,…

A: We will determine the value of the constant a as following.

Q: On the graph of f(x) = = 1? Choose all answers that apply. = cscx and the interval [-2n, 0), for…

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Q: Express the solution as a piecewise-defined function and think about what happens to the graph of…

A: (c) In this question, we have to use the property of the Heaviside unit step function about t=5.…

Q: 7. Determine the equation of the oblique asymptote for the following function. 4x? +7 x – 11 f(x) =…

A: