+0  
 
0
66
3
avatar

I'm still not sure how to do these and I'm getting confused

 

1.

2.

3.

Guest Feb 5, 2018
Sort: 

3+0 Answers

 #1
avatar+85757 
+1

(1)   f(x)  =  3 / [5x^5]

 

If x = 0, the denominator is undefined.....so....the function is defined at all values except at x = 0

 

So....the domain  is    (-inf, 0), U (0, inf)

 

We have   a lower power polynomial in the numerator than in the denominator.....in a Lower/Higher situation, a rational function like this will always have a horizontal asymptote at y  = 0

 

Also....because the power on the variable in the denominator is odd, the function will generate both negative and positve values  in infinite directions both ways

 

So.....the range is     (-inf, 0) U   (0, inf)

 

Here's a graph to check this  : https://www.desmos.com/calculator/4s1yykzw1v

 

 

cool cool cool

CPhill  Feb 5, 2018
 #2
avatar+85757 
+1

(2)  

 

f(x)  =   3 / [ x - 2 ]  + 9

 

The function will be undefined when x  = 2  [ it makes a denominator = 0]

 

Also...... we have a lower power polynomial over a higher power polynomial in the first fraction..... like the first problem, this sets up a horiontal asymptote at y  = 0

 

However, the appended  "9"  shifts this asymptote up 9 units

 

So....we will have a horizontal asymptote at y  = 9

 

Here's a graph to confirm our suspicions :  https://www.desmos.com/calculator/p9km2zdfff

 

 

 

cool cool cool

CPhill  Feb 5, 2018
 #3
avatar+85757 
+1

(3)

 

f(x)  =  [ x^2  - 49]  / [ x + 7]         factor  the denominator

 

f(x)  =   [   ( x + 7) ( x - 7) ]  / ( x + 7)        this simplifies to

 

f(x)  =  x - 7

 

This is a line with a y intercept at  -7

 

Also......  x  = -7    will make the original denominator  0, so this is will the "hole" will occur

 

So.....the first graph is correct

 

 

 

cool cool cool

CPhill  Feb 5, 2018

24 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details