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: 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: (За — 4) (z—2)(ӕ+1) (а- 2) (—3)(4г— 1) express your answer as a fraction "a/b" or a decimal. Let f…

A:

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

A:

Q: Find the flat asymptotes of the functions, if they exist:

A: Given:   a fx=1x2-1    b fx=1x-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…

A:

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: 2. For the rational function f(x)= 2x2-2x-12 %3D x+3x-18 A. Find the domain of the function using…

A: The given rational function is,

Q: Create a rational function, called F(x), that has: a point discontinuity (hole) At least one…

A: soution is given below

Q: 2. If f(x) = e 3x a) Graph f(x) b) Identify the horizontal asymptote of f(x) c) What is the range of…

A:

Q: 200 Calculate > j. Hint: Write as a difference of two sums and use formula (3). j=101

A:

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 -…

A:

Q: Please help me with every question :)

A: Here we have to choose the correct option.

Q: A rational function has the following characteristics: • A domain of [xx-3, x4, x ER} of [y]y = 1.y…

A: The rational function has the following properties, A domain of x|x≠-3, x≠4, x∈ℝ. A range of y|y≠1,…

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

A:

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…

A:

Q: Q2 Consider the function F(x)=2x-1-2 a) Graph Function b) Label at least 3 points C) Label the…

A: Fx=2x-1-2

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…