Question

@Whitemonsterbunny17 I need serious math help with asymptotes of functions and stuff.

Answer 1

I can't stop thinking about this math problem its driving me crazy!

Answer 2

me neither

Answer 3

Lol. @satellite73 My question is about a specific function/graph that changes so much with just an extra constant of 10.

Answer 4

If you go to https://www.desmos.com/calculator and graph these 2 functions, you will see my problem!
\[\frac{ 2x+1 }{ x+3} and \frac{ 2x+11 }{ x+3 }\]
How does adding a constant of only 10 change the function so much? @Whitemonsterbunny17

Answer 5

Here is the picture
@Whitemonsterbunny17 @satellite73

Answer 6

Please help me @mathslover @phi @the_fizicx99 @ipwnbunnies

Answer 7

@madyhughes

Answer 8

i was tagging myself?

Answer 9

ok

Answer 10

Sorry i dont quite understand what you're supposed to be doing.

Answer 11

this is certainly not the graph of a function is it?

Answer 12

Try 2x+6 in the numerator!

Answer 13

Let f(x) = (2x + k) / (x + 3).
Domain of f(x) excludes x = -3 where there is a vertical asymptote.

f'(x) = { (x+3)(2) - (2x + k)(1) } / (x+3)^2 = (2x + 6 - 2x - k) / (x+3)^2
f'(x) = (6-k) / (x+3)^2

The denominator is ALWAYS positive in the domain of the function. (that is, x = -3 is excluded)

The numerator is positive IF k < 6 and negative if k > 6.

Therefore, f(x) is an increasing function if k < 6 and
f(x) is a decreasing function if k > 6.

f(x) is undefined at x = -3

In your first function you had k = 1 and therefore it is always an increasing function.

In your second function you had k = 11 and therefore it is always an decreasing function.

Hence these two graph differently.

Answer 14

Never mind, I understand now. The graph is of 2 functions, Each one a different color.

Answer 15

Aum wins the medal for most rigorous explaination!

Answer 16

Yay for aum!!! :D

Answer 17

Thanks! :D