Rational functions Determine
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Calculus: Early Transcendentals, Books a la Carte Plus MyLab Math/MyLab Statistics Student Access Kit (2nd Edition)
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Calculus and Its Applications (11th Edition)
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- S-20 Rational Function Is y=x3+4x2+x+1 is a rational function?arrow_forward2(1) Calculate well & Show your work. Find: A) Rational function that is the opposite of the given function. B) Coordinates at the origin of the function given. C) Vertical and horizontal asymptotes of the function given. D) The domain of the function given.arrow_forwardA rational function is given. r(x) = 4x + 1 x − 6 (a) Complete each table for the function. (Round your answers to three decimal places where applicable.) Table 1 Table 2 x r(x) 5.5 5.9 5.99 5.999 x r(x) 6.5 6.1 6.01 6.001 Table 3 Table 4 x r(x) 10 50 100 1000 x r(x) −10 −50 −100 −1000 (b) Describe the behavior of the function near its vertical asymptote, based on Tables 1 and 2. r(x) → as x → 6− and r(x) → as x → 6+. (c) Determine the horizontal asymptote, based on Tables 3 and 4. y = From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an answer does not exist, enter DNE. Enter your asymptotes as a comma-separated list of equations if necessary.) x-intercept (x, y) = y-intercept (x, y) =…arrow_forward
- lim x-->3 f(x)=8 and lim x--->3 g(x)= -4 1) limx--->3 (3f(x)-5g(x)) 2) lim x---> G(x)^3 + 50 / ( 5f(x)^(2/3) )arrow_forwardA function is a ratio of quadratic functions and has a verticalasymptote x =4 and just one -intercept, x =1 . It isknown f that has a removable discontinuity at x =- 1 and lim x->-1f(x) = 2. Evaluate a) f (0) b) limx->∞f(x)arrow_forwardf(x) = x+3/x^2-9 find domain: vertical asymptotes l: x=horizontal asymptotes: y=arrow_forward
- A rational function is given. r(x) = x/x-8 (a) Complete each table for the function. (Round your answers to three decimal places where applicable.) Table 1 Table 2 x r(x) 7.5 7.9 7.99 7.999 x r(x) 8.5 8.1 8.01 8.001 Table 3 Table 4 x r(x) 10 50 100 1000 x r(x) −10 −50 −100 −1000 (b) Describe the behavior of the function near its vertical asymptote, based on Tables 1 and 2. r(x) → as x → 8− and r(x) → as x → 8+. (c) Determine the horizontal asymptote, based on Tables 3 and 4. y =arrow_forwardA rational function f(x) has one vertical asymptote x= 2, and one horizontal asymptote, y= -3 and the graph passes through the ordered pair (5,0). Which of the following rational functions satisfy these given properties?arrow_forwardA rational function is given. r(x) = x/x-7 (a) Complete each table for the function. (Round your answers to three decimal places where applicable.) Table 1 Table 2 x r(x) 6.5 6.9 6.99 6.999 x r(x) 7.5 7.1 7.01 7.001 Table 3 Table 4 x r(x) 10 50 100 1000 x r(x) −10 −50 −100 −1000 (b) Describe the behavior of the function near its vertical asymptote, based on Tables 1 and 2. (c) Determine the horizontal asymptote, based on Tables 3 and 4.arrow_forward
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