a Consider the function f(z) = z2 + 11z + 28 z +3 i. Determine the horizontal as

Question

a Consider the function f(z) = z2 + 11z + 28 z +3 i. Determine the horizontal asymptote. If there is no horizontal asymptote, write DNE -3 Preview -3=-3. Preview DNE ii. Determine the roots of the function f. Separate multiple answers with a comma. If there are no roots, write DNE Preview iv. Determine the vertical intercept of the function f. If there is no vertical intercept, write DNE. f(0) = Preview b. Consider the function g(z) = 02 21 i. Determine the horizontal asymptote. If there is no horizontal asymptote, write DNE Preview ii. Determine the vertical asymptote (s). Separate multiple answers with a comma. If there is no vertical asymptote, write DNE. Preview ii. Determine the roots of the function f Separate multiple answers with a comma. If there are no roots, write DNE. Preview iv. Determine the vertical intercept of the function f. If there is no vertical intercept, write DNE. g(0) = 1 Preview

Explanation / Answer

a)    f(x) = (x^2 + 11x + 28)/(x + 3)

i) Horizontal asymptote ======> y = x + 8

ii) Vertical Asymptote =======> x = -3

iii) Roots =====> f(x) = 0 = (x^2 + 11x + 28)

(x + 4)(x + 7) = 0 ======> x = -4, -7

iv) Vertical intercept =======> (0,28/3)

b) f(x) = (x^2 + 10x + 21)/(x^2 + 2)

i) Horizontal asymptote ======> y = 1

ii) Vertical Asymptote =======> None

iii) Roots =====> f(x) = 0 = (x^2 + 10x + 21)

(x + 3)(x + 7) = 0 ======> x = -3, -7

iv) Vertical intercept =======> (0, 21/2)

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