Answer:
At x = 2 does the graph of the following function F(x) have a vertical asymptote
Step-by-step explanation:
To find the Vertical asymptotote of the rational function, we set the denominator equals to 0.
Given the function:
[tex]F(x) = \frac{2}{x-2}[/tex]
Denominator of the fucntion F(x) = x-2
By definition Vertical asymptotote we have;
Denominator of F(x) = 0 i.,e
x-2 = 0
Add 2 to both sides we get;
x = 2
Therefore, at x = 2 does the graph of the following function F(x) have a vertical asymptote
The vertical asymptote of the function [tex]F\left( x \right) = \dfrac{2}{{x - 2}}[/tex] is [tex]\boxed{x = 2}[/tex].
Further explanation:
If rational function [tex]f[/tex] defined as [tex]f\left( x \right) = \dfrac{{p\left( x \right)}}{{q\left( x \right)}}[/tex]
Here, [tex]p\left( x \right)\,\,{\text{and }}q\left( x \right)[/tex] does not have any common factor other than 1. If [tex]c[/tex] is a real zero of [tex]q\left( x \right)[/tex] that is denominator, then [tex]x = c[/tex] is a vertical asymptotes of the graph of [tex]f[/tex].
Given:
The rational function is [tex]F\left( x \right) = \dfrac{2}{{x - 2}}[/tex]
Explanation:
The vertical asymptote is point at which the function is not defined.
The value of the denominator is 0 at [tex]x=2[/tex].
[tex]\begin{aligned}F\left( 0 \right) &= \frac{2}{{2 - 2}} \\ &= \frac{2}{0} \\ &= \infty \\ \end{aligned}[/tex]
The function is not defined if the value of [tex]x = 2[/tex].
The vertical asymptote of the function [tex]F\left( x \right) = \dfrac{2}{{x - 2}}[/tex] is [tex]\boxed{x = 2}[/tex].
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Trigonometry
Keywords: Asymptote, F(x)=2/x-2, vertical asymptote, horizontal asymptote, function, graph.
