Quiz: Q 8 his 6 4016 (0 complete) Analyze the graph of the function 2x-8 H(x)-16

Question

Quiz: Q 8 his 6 4016 (0 complete) Analyze the graph of the function 2x-8 H(x)-16-X2 Factor the numerator and denominator of HO) H(x)-U (Do not simplify.) What is the domain of H(x? Select the correct choice below and, if necessary,fil in the answer OA xx (Type an integer or a simplified fraction) Type an integer or a simplified fraction. Use a comma to separate answers as needed) oc. {xtx2 (Type an integer or a simplified fraction.) 0 D. All real numbers Write H(x) in lowest terms. H(x) = (Simplify your answer.) Locate the intercepts) of the graph. Select the correct choice below and, if necessary, fill in the answer box to c omplete your choice O A. The intercept(s) is/are Simplify your answer Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed) O B. There is no intercept Determine the behavior of the araph of Click to select your answer(s) H at anv x-intercents. Select the correct choice below and. if necessarv fllin anv answer boxes to comoiete vour choi anv x-intercepts lect the correct choice below and. if necessar flli anv answer boxes to comolete vour O Tune here to search oe

Explanation / Answer

H(x) = ( 2x - 8 ) / ( 16 - x^2 )

a) domain of H(x) is { x | x not equal to 4 , -4 }

b) H(x) in lowest terms is

- 2 ( x- 4 ) / ( x - 4 ) ( x + 4 )

= - 2 / ( x + 4)

c) the intercepts is ( 0 , -1/2 )

d) there are no x intercepts

e) vertical asymptotes are x = -4

f) it approaches infinity on one side of the asymtote at x = -4 and - infinity on other side

g) horizontal asymptote is y = 0

h) the graph of H is above the x axis on the interval ( -infinity , -4 ) and below the x axis on the interval ( - 4 , infinity )

i) graph d is correct

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