What are the equations of the asymptotes of the rational function?

f(x)=x^2+2x−3/2x^2−x−1

Vertical asymptotes :

Horizontal asymptote :

Step-by-step explanation:

Consider the given rational function as,

Now, to find the vertical asymptotes of the given rational function, we will first set the denominator of given rational function equal to 0 and then solve. The values at which the denominator becomes 0 gives us the vertical asyptotes of the given rational function.

Now, denominator of given rational function = g(x) = 2x²- x - 1

Now, to find vertical asymptotes, we will set g(x) = 0

∴ 2x² - x - 1 = 0

⇒2x² - 2x + x - 1 = 0

⇒2x(x - 1) + 1(x - 1) = 0

⇒(2x + 1)(x - 1) = 0

⇒2x + 1 = 0  or  x - 1 = 0

So, and are the equations of vertical asymptotes of the given rational function.

In the given rational function, the degree of numerator i.e. f(x) is equal to the degree of denominator i.e. g(x), so the given rational function will have a horizontal asymptote that is given by,

So, is the equation of horizontal asymptote of the given rational function.

50*10 is greater

step-by-step explanation:

if you add the zero from 10 to 50, it will give you a bigger number.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: