ch the graph of the given rational function. Use the graph to complete the follo
ID: 2913327 • Letter: C
Question
ch the graph of the given rational function. Use the graph to complete the following. If they do not exist or if any blanks are empty, enter DNE in all capital letters.
f (x) = 8 divided by x?10 8 / x - 10
(a) The zeros of f (x) : _____ ______
(b) The y - intercept of f (x) : ( 0, ____)
(c) Holes of f (x) : ( ____ , _____ )
(d) Vertical asymptotes of f (x) : x = ________
(e) Horizontal asymptotes of f (x) : y = ________
(f) Slant asymptotes of f (x) : y = _________
(g) Points at which the graph of f (x) crosses the horizontal asymptotes : ( ______ , _____)
(h) The domain of f (x) :
(j) Interval(s) on which f (x) is increasing:
(k) Interval(s) on which f(x) is decreasing:
(l) Interval(s) on which f(x)>0
(m) Interval(s) on which f(x)<0:
Explanation / Answer
f(x) = 8 / ( x- 10 )
a) zeros of f(x) are DNE
b) y intercept is ( 0 , - 4/5 )
c) holes of f(x) = DNE
d) vertical asymptotes
x = 10
e) horizontal asymptote y = 0
f) slant asymptote DNE
g) points at which graph crosses horizontal asymptote DNE
h) domain of f(x) = ( - infinity , 10 ) U ( 10 , infinity )
j) intervals of increasing DNE
k) intervals of decreasing ( - infinity , 10 ) U ( 10 , infinity )
l) f(x) > 0 at ( 10 , infinity )
m) f(x) < 0 at ( -infinity , 10 )
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