Consider a rational function f(r), given by P(x) q(z)' where the degrees of p(r) and q(r) are m and n, respectively. EXPLAIN how to calculate the horizon asymptote of f(r) in the following cases:

Q: determine the value of "a" so that f(x) (image) have the line y=x+5 as an asymptote

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Q: Consider the follo y = (x + 8) (x + 3)/(x - 1)² (a) Find the domain, x- and y-intercepts, vertical…

A: This is a question about sketching a curve  by analyzing of behavior of the  function .

Q: Find the vertical asymptotes of the rational function. 12) F(x)=- x2-16 x2 + 5x+4 A)x= -1, x=-4 B)…

A: Given           F(x)=x2-16x2+5x+4 Now, Factorize the numerator and denominator…

Q: t. determine just one horizontal asymptote of f() by computing an appropiorate llmit. f(x)= V4x^+ qx…

A: Find the value for f(x) as x tends to inf.

Q: Create a rational function that has a vertical asymptote at x=2, a horizontal asymptote at y=-3 and…

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Q: For f(x)= 2x2/x2-1 find, using calculus, horizontal and vertical asymptotes, where the curve…

A: Given, f(x)=2x2x2-1

Q: 2x+2x+1 Q2) Find the asymptotes for the following functions : f(x)= g(x) =

A: We have been given the two functions f(x)=2x2+2x+12xg(x)=x2-11+x2

Q: 9. For the function f(x) x2–25 x2 –3x–10 a) What is the vertical asymptote? b) What is the…

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Q: Find all vertical asymptotes and horizontal asymptotes of the given function: f (x) = ²+16 x2+4x+5 O…

A: Please check your question and options.

Q: If f has a vertical asymptote at x = c then f(c) does not exist. True False

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

Q: 1. (S8.Purple) Consider the following rational function (x² – x)(x+6) (x – 1)(x+7)(x– 8) r(x) (a)…

A: (a) domain of r(x)…

Q: Q1) Graph the following rational function, labeling clearly all intercepts and asymptotes. R(x) = x…

A: We will find intercept and asymptote and will use them to plot graph

Q: x2 10. Consider f (x) x²–4' State the vertical and horizontal asymptotes. b. Find the domain of f…

A: The given function is fx=x2x2-4. (a) Obtain the vertical asymptotes as follows: Take the…

Q: Find the limit of the rational function (a) as x→∞ and (b) as x→→ ∞. 4 3 2x + 5x - 1 f(x) = 2 2x -…

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Q: Which of the following functions has exactly one vertical asymptote when graphed? a) f(x) b) f(x):…

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Q: x2 – 4 - a) f(x) = b) f(x) = x + 1 1 i) Find the domain and, if any, the intercepts of f(x). ii) If…

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Q: Find (with justification) the vertical and horizontal asymptotes of the function f(x) (show all…

A: Let's find.

Q: Let f(x) be the function defirted as x² - 2ax + a² f(x) = (x – b)(x + c)’ where a, b and c are…

A: Given function,  a, b,c are constants in ℝ.  To find the  Horizontal and  vertical asymptotes of…