Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To determine where the function [tex]\( F(x) = \frac{1}{x(x+6)(x-1)} \)[/tex] has vertical asymptotes, we need to find the values of [tex]\( x \)[/tex] that make the denominator zero. The function will be undefined at these values, leading to vertical asymptotes.
We start by setting the denominator equal to zero:
[tex]\[ x(x+6)(x-1) = 0 \][/tex]
Now, solve for [tex]\( x \)[/tex] by finding the roots of each factor individually:
1. Setting [tex]\( x = 0 \)[/tex]:
[tex]\[ 0 \cdot (0+6) \cdot (0-1) = 0 \][/tex]
So, [tex]\( x = 0 \)[/tex] is a root.
2. Setting [tex]\( x+6 = 0 \)[/tex]:
[tex]\[ (x+6) = 0 \][/tex]
[tex]\[ x = -6 \][/tex]
So, [tex]\( x = -6 \)[/tex] is another root.
3. Setting [tex]\( x-1 = 0 \)[/tex]:
[tex]\[ (x-1) = 0 \][/tex]
[tex]\[ x = 1 \][/tex]
So, [tex]\( x = 1 \)[/tex] is another root.
Thus, the values of [tex]\( x \)[/tex] that make the denominator zero, and hence where vertical asymptotes occur, are [tex]\( x = 0 \)[/tex], [tex]\( x = 1 \)[/tex], and [tex]\( x = -6 \)[/tex].
The correct answers are:
A. 1
C. 0
E. -6
We start by setting the denominator equal to zero:
[tex]\[ x(x+6)(x-1) = 0 \][/tex]
Now, solve for [tex]\( x \)[/tex] by finding the roots of each factor individually:
1. Setting [tex]\( x = 0 \)[/tex]:
[tex]\[ 0 \cdot (0+6) \cdot (0-1) = 0 \][/tex]
So, [tex]\( x = 0 \)[/tex] is a root.
2. Setting [tex]\( x+6 = 0 \)[/tex]:
[tex]\[ (x+6) = 0 \][/tex]
[tex]\[ x = -6 \][/tex]
So, [tex]\( x = -6 \)[/tex] is another root.
3. Setting [tex]\( x-1 = 0 \)[/tex]:
[tex]\[ (x-1) = 0 \][/tex]
[tex]\[ x = 1 \][/tex]
So, [tex]\( x = 1 \)[/tex] is another root.
Thus, the values of [tex]\( x \)[/tex] that make the denominator zero, and hence where vertical asymptotes occur, are [tex]\( x = 0 \)[/tex], [tex]\( x = 1 \)[/tex], and [tex]\( x = -6 \)[/tex].
The correct answers are:
A. 1
C. 0
E. -6
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.