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.
In Exercises15–36, find the points of inflection and discuss theconcavity of the graph of the function.
f(x)=\frac{6-x}{\sqrt{x}}
Exercises 101–103 will help you prepare for the material covered in
the next section. Use the graph of function f to solve each exercise.
5-
4-
3-
2-
1-
-5-4
1 2 3 45
y = flx)
101. For what values of x is the function undefined?
102. Write the equation of the vertical asymptote, or the
vertical line that the graph of f approaches but does not
touch.
103. Write the equation of the horizontal asymptote, or the
horizontal line that the graph of f approaches but does not
touch.
In Exercises 65–70, use
the graph of f to find each
indicated function value.
y = f(x)
65. f(-2)
66. f(2)
-5 -4--2
2 4 5
67. f(4)
68. f(-4)
69. f(-3)
70. f(-1)
Chapter 3 Solutions
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