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Reciprocal functions
Inverse variation is described by reciprocal functions.
Plot the data shown in the table and sketch a reciprocal
curve to fit the data.
p = 1/V
What is the domain for the sketched curve?
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Direct or inverse variation?
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General form
general reciprocal function:
f (x) =
a
x–h
+k
vertical asymptote: x = h
horizontal asymptote: f (x) = k
domain: x ∈ (–∞,h)∪(h,∞)
range: f (x) ∈ (–∞,k)∪(k,∞)
roots: x = –a/k + h
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Finding vertical and horizontal asymptotes
A vertical asymptote in a reciprocal function occurs where it is
undefined – where the denominator is zero.
Show that the vertical asymptote of a
general reciprocal function is x = h.
equate the denominator to zero:
solve for x:
f (x) =
a
x–h
+k
x–h=0
x=h 
To understand why a horizontal asymptote occurs, examine
the behavior of the function as x becomes very large.
Explain why the horizontal asymptote
of a general reciprocal function is y = k.
f (x) =
a
x–h
+k
x is in the denominator, and as the denominator of a fraction
become much larger than the numerator, the fraction tends to
zero, but does not affect the constant k.
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Asymptotes of reciprocal functions
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