In Exercises 130–133, write the equation of a rational function f ( x ) = p ( x ) q ( x ) having the indicated properties, in which the degrees of p and q are as small as possible. More than one correct function may be possible. Graph your function using a graphing utility to verify that it has the required properties. 132. f has a vertical asymptote given by x = 1, a slant asymptote whose equation is y = x , y -intercept at 2, and x -intercepts at −1 and 2.
In Exercises 130–133, write the equation of a rational function f ( x ) = p ( x ) q ( x ) having the indicated properties, in which the degrees of p and q are as small as possible. More than one correct function may be possible. Graph your function using a graphing utility to verify that it has the required properties. 132. f has a vertical asymptote given by x = 1, a slant asymptote whose equation is y = x , y -intercept at 2, and x -intercepts at −1 and 2.
Solution Summary: The author explains the required properties of a rational function, such as f's vertical asymptote, slant, and x- intercepts, by sketching the graph using graphing utility.
In Exercises 130–133, write the equation of a rational function
f
(
x
)
=
p
(
x
)
q
(
x
)
having the indicated properties, in which the degrees of p and q are as small as possible. More than one correct function may be possible. Graph your function using a graphing utility to verify that it has the required properties.
132.f has a vertical asymptote given by x = 1, a slant asymptote whose equation is y = x, y-intercept at 2, and x-intercepts at −1 and 2.
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