Question

g(x)=log(x+5)
description of transformation
equations for the vertical asymptote(s)
x-intercept in (x,y) form

Answer 1

start with f(x)=log(x) and shift it 5 units to the left to get g(x)=log(x+5)

vertical asymptote is x = -5 (since this is the value that makes the argument x+5 equal to zero)

x-intercept is (-4,0) and you can find this by plugging in g(x)=0 and solving for x

g(x)=log(x+5)
0=log(x+5)
10^1=x+5
1=x+5
1-5=x
-4=x
x=-4

so again, the x-intercept is (-4,0)

Answer 2

same thing g(x)=log(-x)
description of transformation
equation
(x,y)

Answer 3

start with g(x)=log(x) and reflect it over the y-axis to get g(x)=log(-x)

vertical asymptote is x=0

x-intercept is (-1,0)

Answer 4

did you mean start with f(x)=log(x) on the first step

Answer 5

so there really is no transformation right

Answer 6

the transformation is the reflection over the y-axis

Answer 7

yes, you usually start with the parent function, which in this case is f(x)=log(x)

Answer 8

ok thanks
You explained it very well thank you.