## haleyelizabeth2017 one year ago Determine the equation of the horizontal asymptotes, if any, of the function. f(x)=4/x^2+1)

1. jim_thompson5910

it's this right? $\Large f(x) = \frac{4}{x^2+1}$

2. haleyelizabeth2017

Yes :)

3. jim_thompson5910

|dw:1444170111505:dw|

4. jim_thompson5910

rewrite 4 as 4*1 |dw:1444170139532:dw|

5. jim_thompson5910

the 1 up top can be written as $$\Large x^0$$ |dw:1444170171324:dw|

6. jim_thompson5910

the largest exponent for the numerator is 0 so the degree of the numerator is 0 the largest exponent for the denominator is 2 so the degree of the denominator is 2 |dw:1444170219440:dw|

7. jim_thompson5910

Rule: If the degree of the numerator is smaller than the degree of the denominator, then the horizontal asymptote is always the line y = 0. Basically the x axis

8. jim_thompson5910

the denominator grows far faster than the numerator so as x gets larger, f(x) approaches 0 |dw:1444170311640:dw| it never actually gets to 0 though

9. haleyelizabeth2017

Good rule to know.