Question

Describe the transformation from f(x)=a^x to f(x)=b^x where 1 13 years ago

Answer 1

graphs have same shape but slope is greater with the a^x (it increases at faster rate)

Answer 2

I was asking for more along the lines of vertical stretch, horizontal stretch, etc.

Answer 3

its a horizontal stretch, relatively to the parent.
for example
y = 2^x , y = .5 ^ x

Answer 4

by what factor?

Answer 5

a ^[ x * ln b / ln a ] = b^x

Answer 6

how did you get that?

Answer 7

look at easier examples, comparing y = 2^x and y = 2^(2x)

Answer 8

ok here is a general rule

Answer 9

you ready ?

Answer 10

if you start with f(x) , f (ax) does a horizontal stretch/shrink by a factor of 1/a. it depends on a, and we assume a > 0 . if 0<a<1, then its a horizontal stretch because if a < 1 then 1/a > 1 , and if a > 1 , then it is a horizontal shrink because 1/a < 1

Answer 11

so it becomes clear if its a stretch or a shrink because of the factor itself. if the factor is less than 1, then its a shrink. if its greater than 1 its a stretch

Answer 12

now we started with f(x) = a^x , then f ( ln b/ ln a * x ) = a ^ (ln b / ln a * x ) = b^x .
so f(x) is stretched or shrinked by a factor of ln a / ln b (the reciprocal )

Answer 13

the important thing is that it is horizontal

Answer 14

you there ?

Answer 15

I understand the picture but I don't understand how that translated into lnb/lna

Answer 16

the 1st picture