Answer the question. Show ALL your steps in your calculations. Answer in complete sentences. Answer the question. Show ALL your steps in your calculations. Answer in complete sentences.2x2-50108 (x)=x2+8x+15Holes :2x²–501²+8x+152(x+5Xx-5)(x+5)(x+3)8 (x) =-10t0If there is the same factor in the numerator and denominator, then- 30++5there is hole.common factor is (x+ 5)hole is at x = -5Domain :Asymptotes :8 (x) = 42-50%3Dx+8x+152(x+5)(x-5)(x+5Xx+3)2x-502(x-5)2(1-25)2(x+5)(x-5)8(x) =8 (x) = -2x-50x+5x+3x+15x²+8x+15(x+3)x(x+5)+3(x+5)(x+5)x+3)2(x-5)denominator is zero at x = -38 (x) =a+3)Vertical asymptoe : x = -3g (x) =8 (x) is defined at all values except x = -32x-50Therefore, Domain is (-0, –3) U(-3, 00)x2+8x+15Range :(2)If we look at the graph of g (x), function is taking all values except= 2lim(1+*+4)Horizontal asymptote : y = 2y = limy = 2=(1++)Therfore, range of g (x) is (-,2) U (2, 0).Find the following analyses of the function:Fill out the following chart by using the Vertical asymptotes and hole x values for theinterval:f(x)f(x)f"(x)

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Answer the question. Show ALL your steps in your calculations. Answer in complete sentences. 8 (x)=_2r²–50 x2+8x+15 10 Holes : 2x²–50 x²+8x+15 2(x+5Xx=5) a+5)(x+3) 8 (x) = to - 30 10 If there is the same factor in the numerator and denominator, then there is hole. common factor is (x + 5) hole is at x = -5 Domain : Asymptotes : g (x) = 22-50 x?+8x+15 8(x) = 2'-50 x²+8x+ 15 2(x+ 5){x-5) (x+5X(x+3) 2(x-5) 22-50 x+5x+3a+15 2(1²–25) 2(x+5x-5) (+3) 8 (x) = (x+5)(x+3) denominator is zero at x = -3 g (x) = 20-5) (+3) Vertical asymptoe : x = -3 8 (x) is defined at all values except x = -3 Therefore, Domain is (-0,–3) U(-3, o0) Range : If we look at the graph of g (x), function is taking all values except y = 2 g (x) = 2-50 x²+8x+15 () y = lim x*(1++) = = 2 lim (1+*+4) Therfore, range of g (x) is (-∞, 2) U (2, 0). Horizontal asymptote : y = 2

Answer the question. Show ALL your steps in your calculations. Answer in complete sentences. 8 (x)=_2r²–50 x2+8x+15 10 Holes : 2x²–50 x²+8x+15 2(x+5Xx=5) a+5)(x+3) 8 (x) = to - 30 10 If there is the same factor in the numerator and denominator, then there is hole. common factor is (x + 5) hole is at x = -5 Domain : Asymptotes : g (x) = 22-50 x?+8x+15 8(x) = 2'-50 x²+8x+ 15 2(x+ 5){x-5) (x+5X(x+3) 2(x-5) 22-50 x+5x+3a+15 2(1²–25) 2(x+5x-5) (+3) 8 (x) = (x+5)(x+3) denominator is zero at x = -3 g (x) = 20-5) (+3) Vertical asymptoe : x = -3 8 (x) is defined at all values except x = -3 Therefore, Domain is (-0,–3) U(-3, o0) Range : If we look at the graph of g (x), function is taking all values except y = 2 g (x) = 2-50 x²+8x+15 () y = lim x(1++) = = 2 lim (1++4) Therfore, range of g (x) is (-∞, 2) U (2, 0). Horizontal asymptote : y = 2

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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