Question

what is the equation of the vertical asymptotes of the graph g(x)=-log(x)+2

Answer 1

when is log(x) undefined?

Answer 2

what?

Answer 3

.... for what values of x, is the log function .... not defined?

Answer 4

f(x)=log(x)

Answer 5

do you recall what a vertical asymptote is?

Answer 6

i dont think so

Answer 7

it should be presented to you in your material ...

Answer 8

if you lok at a graph of the function; it is related to all the values of x that cannot be defined for the function: like 1/x has a vertical asymptote at x=0, since 1/0 cannot be defined

Answer 9

ill just write it all out for you.

describe the transformations on the following graph of f(x)=log(x). state the placement of the vertical symptote and x intercept after the transformation. for example, vertical pellet up 2 or reflected about the x-axis are descriptions.

g(x)=-log(x)+2

Answer 10

it looks like they expect you to have familiarity with the log fucntion in order to address the problem to start with

Answer 11

log(x) has an x intercept at x=1, and a vertical asymptote at x=0

how does the shift alter these properties?

Answer 12

i already have the transformation, its the graph of G(x)=-log(x)+2 reflects across the x axis and upward 5.

Answer 13

+2 is not upward by 5 ...

Answer 14

yah my mistake

Answer 15

g = -logx + 2

0 = b^(-logx + 2)

b^0 = b^(-logx) * b^2

1/b^2 = b^(log(1/x)

1/b^2 = 1/x

x = b^2

Answer 16

in some courses, log is generaic and represents the natural log; in other courses log is a base10 construction

Answer 17

b represents what?

Answer 18

b = base that is consistent with whatever the course defines log to be :)

Answer 19

so the answer is b^2

Answer 20

whatever the base is; the solution would be the square of the base .. yes

Answer 21

0 = 2 - log(x), when x = b^2

0 = 2 - log(b^2)

0 = 2 - 2log(b)

0 = 2 - 2(1)

Answer 22

for my previous function,
g(x)=log(x-5) the vertical asymptote is 5

Answer 23

that looks appropriate yes.

Answer 24

so why is this function so complicated?

Answer 25

the only complication is in the x intercept. they have not shifted the graph left or right; only up and down

you therefore need to define the value of x when g(x)=0

Answer 26

so whats the x intrercept of the function

Answer 27

in general; x = (vertical asymptote) is affected by a left to right shift of +c like this:

x+c = vertical asymptote

x = vertical asymptote - c

Answer 28

i already covered how to determine the x intercept of this function ...

Answer 29

ok i think the x intercept is (0,2)

Answer 30

it wil be (0,b^2) ; so unless your log base is in sqrt2 .... you might want to reconsider that