In the function:  f(x)= 6/((x^2)-16)  Where is the function concave up and down in interval notation?  What are the inflection points of the function?  What are the vertical asymptotes of the function?

Q: graph the function using appropriate methods fromthe graphing procedures, identifyingthe coordinates…

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Q: What type of functions are used with asymptotes

A: Explanation: There are three types of asymptotes that tells differently about function. vertical…

Q: On which the interval the function is increasing?

A: Given,          The graph of the function is shown below :

Q: What is the process for determining the horizontal asymptote of a function from its equation?

A: The method used to find the horizontal asymptote changes depending on how the degrees of the…

Q: Compute all the vertical asymptotes of the function x2 + 1 y = Зх— 2х2 Produce the graph of the…

A: Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of the…

Q: Find the asymptotes, intervals of increase, decrease, concave upward, concave downward, local max,…

A: No asymptotes, Increasing when X<3/4 Decreasing when 3/4<X<1 Concave down for x<1 Local…

Q: ASYMPTOTE

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Q: Find the formula for a function that has a vertical asymptotes x=4 and x=6 and a horizontal…

A: The easiest type of function to use for these types of problems are rational unctionsFor vertical…

Q: Sketch the function R(x)=(3x4+15x3-39x2+21x)/ ( 4x3-20x2+25x). Show all work for intercepts,…

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Q: Find any asymptotes and relative extrema that may exist and use a graphing utility to graph the…

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Q: Find the horizontal asymptotes of the function by computing the limits at infinity.

A: Asymptote is a line along which the function tends to infinity or minus infinity. Horizontal…

Q: tion 1. Find the rule of the piecewise function

A: 1. From the graph given , the piecewise distribution of the function is as follows ,  fx=x+1 ,…

Q: find the horizontal asymptotes of the function by computing the limits at infinity.

A: Find the limits at infinity,

Q: Show that f (x) = 2x2 -3 is an even function. Explain why itsgraph is symmetric about the y-axis.

A: Here given fx=2x2-3   A function is said to be an even function if f-x=fx Now…

Q: Find the derivative of the function by the limit process. f(x) = x² + x - 5 f'(x) =| 4x – 8

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Q: Find the exact location of all relative and absolute extrema of the function f(x)= 8x² +48x +9 with…

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Q: Use the alternate definition, lim Ax)-Aa) to determine the instantaneous rate of X- a change of Ax)…

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Q: Suppose a cannon is placed at the origin and elevated at an angle of 60 degrees. If the cannonball…

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Q: Given the function g(x) = – 2x* + 7x" +x2 + r - There are at most x-intercepts, and based on the…

A: For a polynomial P(x) of degree 'n' 1. The maximum number of x-intercepts is given by 'n' 2. The…

Q: Suppose a cannon is placed at the origin and elevated at an angle of 60 degrees. If the cannonball…

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Q: Find the points on the graph of f(x) = 6x – 2x³ where the tangent line is horizontal. (Use symbolic…

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Q: Use second derivative test, If f(x): 3 - 25x + 9 then f(x) has a local maximum at the point = 6 -5…

A: The given function is f(x)=x33-25x+9 Differentiate with respect to x,

Q: Determine the horizontal asymptote. (3x–1)(x+3) (x+2{x-4) f(x)

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Q: Find any asymptotes and relative extrema that may exist and use a graphing utility to graph the…

A: The function is y=lnxx. The vertical asymptote occurs at the points where the function becomes…

Q: Find f'(x). F(x) = x5 – 4x3 + x - 1 f'(x) = Compare the graphs of f and f' and use them to explain…

A: Given, f(x)=x5-4x3+x-1

Q: Write down a function that has vertical asymptotes at the points x=1, x=2, and x=3, and a horizontal…

A: Given The function has vertical asymptotes at the points x=1, x=2, and x=3, and a horizontal…

Q: True or False The cube root function is odd and is decreasing on the interval (-∞,∞).

A: we have to tell whether the given statement is True or False

Q: Find any asymptotes and relative extrema that may exist and use a graphing utility to graph the…

A: The relative extrema is obtained when the first derivative of the function y=lnxx equals zero. The…

Q: What is the Oblique Asymptote of the function?

A: To find the oblique asymptote for f(x)=axm+...bxn+..., m>n we have to take division of…

Q: A function can have two different horizontal asymptotes

A: The given statement is TRUE.A function has two different horizontal asymptotes when…

Q: How can we analyze the graphs of functions having horizontal or vertical asymptotes?

A: Check for when we have vertical and horizontal asymptote

Q: First image is: Is that function diverges or converges? Second image is: Is that function diverges…

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Q: What is the relationship between functions whose limits can be obtained by direct substitution and…

A: We need to define the relation between a limit and continuous function.

Q: find all vertical and horizontal asymptotes algerbraically, f(x)=3x^2-x+5/x^2-4

A: . Find all vertical and horizontal asymptotes algebraically, f(x)=3x^2-x+5/x^2-4For calculating the…

Q: How would you define f(2) in order to make f continuous at 2? limx→2 x^3-8/x^2-4 show ALL of your…

A: Let's solve limit problem.

Q: sketch the graph of the function. Indicate the transition points and asymptotes

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Q: By using intermediate value theorem locate a root for the f(x) = 2x3 - 3x2 - 6.

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Q: Explain why functions with cusps are not differentiable even though they are continuous.

A: Derivative is a slope, defined by a limit.   In order for a derivative to exist, it needs to be…

Q: Find thu constant a such that the function 15 Continuous on thi entire real line. Usinx gex)= a-7x…

A: Here we use the concept of limit

Q: Determine from the graph whether the function has any absolute extreme values on [a, b]. Then…

A: For given graph, Absolute Maximum is at x = d. and  Absolute minimum does not exist.

Q: A wire of length 8x is bent into the shape of a circle. A. Express the circumference of the circle…

A: NOTE: Refresh your page if you can't see any equations. . the total length of the wire is L=8x so…

Q: Explain Why functions with cusps are not differentiable even though they are continuous.

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Q: What are the end-behavior asymptotes for the function f (x) = ? 2z+1

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Q: Sketch the graph of the function. Indicate the asymptotes, local extrema, and the points of…

A: Explanation of the answer is as follows

Q: How can you determine from the equation of a function if it has a vertical asymptote or a hole…

A: First of all we rearrange the given equation of function as rational function. Then factor the…

Q: Find the points on the graph of f(x)=3x-x^3 where the tangent line is horizontal.  (Use symbolic…

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Q: 2. Use the First Derivative Test with a number line to find the local extremes of the function Ax) =…

A: Solved below

Q: Suppose a cannon is placed at the origin and elevated at an angle of 60 degrees. If the cannonball…

A: