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 ) = 2 x + 10 x 2 + 9 x + 20
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 ) = 2 x + 10 x 2 + 9 x + 20
Solution Summary: The author explains the domain of the function f(x)=2x+10x
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.
For Exercises 103–104, given y = f(x),
remainder
a. Divide the numerator by the denominator to write f(x) in the form f(x) = quotient +
divisor
b. Use transformations of y
1
to graph the function.
2x + 7
5х + 11
103. f(x)
104. f(x)
x + 3
x + 2
Exercises 65–74: Use the graph of f to determine intervals
where f is increasing and where f is decreasing.
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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