In what ways can vertical, horizontal, and oblique asymptotes be identified? use your own example to identify.

Lets take an example

f(x) =

In a rational function, the function has vertical asymptotes when denominator =0.

To find out vertical asymptote we will make denominator =0 , to find out for what value of x the function becomes undefined.

x+1=0 so x=-1

Hence vertical asymptote at x=-1

In a rational function, horizontal asymptote can be find using the degrees . We have 3 cases

•If Degree of numerator is less than the denominator degree then horizontal asymptote is y = 0.

•If Degree of numerator is greater than denominator degree then there is no horizontal asymptote . if degree of numerator is greater by a margin of one then there there will be oblique asymptote.

•if Degree of numerator is equal to the denominator degree then the horizontal asymptote is equal to the leading coefficient of numerator to the leading coefficient of denominator.

In our example

f(x) =

Degree of numerator is 1 and degree of denominator is 1

Both are equal so we take ratio of leading coefficients.

So horizontal asymptote y =

Lets take another example

degree of numerator is greater than the denominator degree by a margin of one . so we will have oblique asymptote.

We find oblique asymptote by long division

By long division we will get x

So oblique asympotote is y=x

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles

sas (side angle side)

aa(angle angle)

sss(side side side)

sas you have to find two sides with an angle in between

aa you find two angles because it will always add up to 180

sss find all sides

step-by-step explanation: