F(x)= x-2/ x-4

graph this equation and identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asymptote.

The discontinuity is x = 4

There no holes

The equation of the vertical asymptote is x = 4

The x intercept is 2

The equation of the horizontal asymptote is y = 1

Step-by-step explanation:

* Lets explain the problem

∵

- To find the point of discontinuity put the denominator = 0 and find

 the value of x

∵ The denominator is x - 4

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

* The discontinuity is x = 4

- A hole occurs when a number is both a zero of the numerator

 and denominator

∵ The numerator is x - 2

∵ x - 2 = 0 ⇒ add 2 to both sides

∴ x = 2

∵ The denominator is x - 4

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

∵ There is no common number makes the numerator and denominator

   equal to 0

∴ There no holes

- Vertical asymptotes are vertical lines which correspond to the zeroes  

  of the denominator of the function

∵ The zero of the denominator is x = 4

∴ The equation of the vertical asymptote is x = 4

- x- intercept is the values of x which make f(x) = 0, means the

 intersection points between the graph and the x-axis

∵ f(x) = 0

∴ ⇒ by using cross multiplication

∴ x - 2 = 0 ⇒ add 2 to both sides

∴ x = 2

* The x intercept is 2

- If the highest power of the numerator = the highest power of the

 denominator, then the equation of the horizontal asymptote is

 y = The leading coeff. of numerator/leading coeff. of denominator

∵ The numerator is x - 2

∵ The denominator is x - 4

∵ The leading coefficient of the numerator is 1

∵ The leading coefficient of the denominator is 1

∴ y = 1/1 = 1

* The equation of the horizontal asymptote is y = 1

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights