Question

HELP ME PLEASE I HAVE A FINAL TOMORROW!!!!!

For the following logarithmic function, determine the domain, vertical asymptote, and the x-intercept

f(x)=ln(x+1)

PLEASE, I NEED YOUR HELP, PLEASE

Answer 1

which part are you stuck at ?

Answer 2

`domain` is the set of all values for which the function is defined. logarithmic function is defined only for positive numbers, so simply solve below for domain :
\[\large x+1\gt 0\]

Answer 3

x>-1
therefore -1,infinity

Answer 4

ok there goes the domain
and the VA is x=-1 cause of just solving it

Answer 5

ok so I got domain and VA

Answer 6

NOW, how do you do Intercept again???

Answer 7

Perfect!

Domain : (-1, \(\infty\))
VA : x = -1

Answer 8

thank-you :)

Answer 9

ok so anyways, intercept???

Answer 10

x intercept is the x value that makes the function equal to 0

Answer 11

solve below for x intercept :
\[\ln (x+1) = 0\]

Answer 12

isn't it -1???

Answer 13

plugin x = -1 into the function,
does it spit out 0 ?

Answer 14

yes

Answer 15

careful

Answer 16

\[\ln (x+1) = 0\]

is equivalent to

\[x+1 = e^0\]

which is same as

\[x+1 = 1\]

\[x = ?\]

Answer 17

0

Answer 18

Yep!

Answer 19

you may get more convinced by looking at the graph
https://www.desmos.com/calculator/bs9qbr0fgo

Answer 20

Ok um it said that the Intercept was (0,0) not just 0, so may you explain that please???????

Answer 21

the graph just answered my question, didn't it?

Answer 22

yes, x = 0 is a number
(0, 0) is a point

Answer 23

your textbook is saying the x intercecpt point is (0, 0) which should make sense, eh ?

Answer 24

ohhhhh, I see, thank-you very much and the answer sheet my teacher gave me said that btw

Answer 25

ok and if I may I just just ask how to find the range of this equation: