Question

How do the graphs of y = 1/x and y = 5/x+6 compare?

Answer 1

i just need help doing it, i don't just want the answer

Answer 2

Hello!

Answer 3

hi! can you help?

Answer 4

Sure thing.

Answer 5

Do you have any ideas? Or should we start from scatch?

Answer 6

scratch?

Answer 7

Okay.

Answer 8

First look at y = 1/x

if x is 0 then y= 1/0 Which is undefined. But think like this: instead of 0, let x be a small number like 1/100000
when we divide 1/ (1/100000) we get 100000 (a big number)

the point is as you get close to x=0 y gets really big

when x=1, y =1/1 = 1
when x is really big y = 1/10000 which is close to 0

so here are 3 points
(0, infinity), (1,1), and (infinity, 0)

Answer 9

Look at it like this now, \[ y = \frac{5}{x+6} \]

Answer 10

Got it so far?

Answer 11

\[ y = \frac{5}{x+6} \]
at a certain x value x+6 = -6

Answer 12

i saw this explanation on another post but its kind of confusing. do i have to use 100000

Answer 13

When is y= 1 (to pick a point)
1= 5/(x+6)
Multiply both sides by x+6 to get
x+6= 5
x= -1
so (-1,1) is on the graph
then, when x gets really big y = 5/big number ---> 0

Answer 14

If you still need more help:

http://www.regentsprep.org/Regents/math/algtrig/ATP9/funclesson1.htm

Answer 15

Is the second equation \[y = \dfrac{5}{x}+6 \] or \[y = \dfrac{5}{x+6} \]