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. 131. f has vertical asymptotes given by x = −2 and x = 2, a horizontal asymptote y = 2, y -intercept at 9 2 , x -intercepts at −3 and 3, and y -axis symmetry.
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. 131. f has vertical asymptotes given by x = −2 and x = 2, a horizontal asymptote y = 2, y -intercept at 9 2 , x -intercepts at −3 and 3, and y -axis symmetry.
Solution Summary: The author explains how to graph a rational function using graphing utility to verify that it has the required properties or not.
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.
131.f has vertical asymptotes given by x = −2 and x = 2, a horizontal asymptote y = 2, y-intercept at
9
2
, x-intercepts at −3 and 3, and y-axis symmetry.
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 1–6, find the domain and range of each function.1. ƒ(x) = 1 + x2 2. ƒ(x) = 1 - 2x3. F(x) = sqrt(5x + 10) 4. g(x) = sqrt(x2 - 3x)5. ƒ(t) = 4/3 - t6. G(t) = 2/t2 - 16
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