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 in interval notation. b . Simplify the rational expression defining the function. c. Identify any vertical asymptotes. d . Identify any other values of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous. e . Identify the graph of the function. f ( x ) = x 2 + x − 6 x − 2
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 in interval notation. b . Simplify the rational expression defining the function. c. Identify any vertical asymptotes. d . Identify any other values of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous. e . Identify the graph of the function. f ( x ) = x 2 + x − 6 x − 2
Solution Summary: The author explains that the domain of the function f(x)=x
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 in interval notation.
b. Simplify the rational expression defining the function.
c. Identify any vertical asymptotes.
d. Identify any other values of x (other than those corresponding to vertical asymptotes) for which the function is discontinuous.
In Exercises 20–22, find the domain of each function.
20. f(x) = 7x - 3
1
21. g(x)
x + 8
3x
22. f(x) = x +
x - 5
Find the domain and range of f(x) = 3(9x +7)2 – 7.
Express your answer in interval notation using exact values.
The diagram below gives part of the graph of function f.. For a<x<b, all of the following are true:
f(x)<0 , f′(x)>0 and |x|<12
Find a and b.
Write your answer in the form a, b without spaces, e.g. for a=−4 and b=3 write −4,3.
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