The rational functions studied in this section all have the characteristic that the numerator and denominator do not share a common variable factor. We now investigate rational functions for which this is not the case. For Exercises 111-114, a. Write the domain of f interval notation. b. Simplify the rational expression defining the function. c. Identify any vertical asymptotes. d. Identify any other value of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous. e. Identify the graph of the function. f x = 2 x − 2 x 2 + 2 x − 3
The rational functions studied in this section all have the characteristic that the numerator and denominator do not share a common variable factor. We now investigate rational functions for which this is not the case. For Exercises 111-114, a. Write the domain of f interval notation. b. Simplify the rational expression defining the function. c. Identify any vertical asymptotes. d. Identify any other value of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous. e. Identify the graph of the function. f x = 2 x − 2 x 2 + 2 x − 3
Solution Summary: The author explains how to determine the domain of f in the interval notation for the function.
The rational functions studied in this section all have the characteristic that the numerator and denominator do not share a common variable factor. We now investigate rational functions for which this is not the case. For Exercises 111-114,
a. Write the domain of f interval notation.
b. Simplify the rational expression defining the function.
c. Identify any vertical asymptotes.
d. Identify any other value of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous.
Decide whether each limit exists. If a limit exists, estimate its
value.
11. (a) lim f(x)
x-3
f(x) ↑
4
3-
2+
(b) lim f(x)
x―0
-2
0
X
1234
Determine whether the lines
L₁ (t) = (-2,3, −1)t + (0,2,-3) and
L2 p(s) = (2, −3, 1)s + (-10, 17, -8)
intersect. If they do, find the point of intersection.
Convert the line given by the parametric equations y(t)
Enter the symmetric equations in alphabetic order.
(x(t)
= -4+6t
= 3-t
(z(t)
=
5-7t
to symmetric equations.
Elementary Statistics: Picturing the World (7th Edition)
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