Question

real quick:
if a exponential function has a vertical shift is it still exponential?

Answer 1

@darkknight, could you explain how it would stop being exponential as a result of a vertical shift? If it is no longer an exponential function, what kind of function is it after the vertical shift?

Answer 2

sorry what i meant was that it wouldn't have that standard exponential form right

Answer 3

If it shifts vertically, then yes only the form would change. It would no longer be in standard form. Do you have an idea of which transformation preserves the standard form?

Answer 4

yes sir

Answer 5

vertical dilations, because that would be multiplying to Ao
horizontal dilations and shifts

Answer 6

maybe

Answer 7

I'm not sure about the horizontal shifts and dilations actually

Answer 8

Okay, Vertical dilation should be correct.

Answer 9

what about horizontal shifts and dilations?

Answer 10

shifts would effect it like this 4^x would be 4^(x-1) if shift 1 to the right

Answer 11

and for dilations it will be f(x/c)

Answer 12

so would Ao (b)^(t-1) be considered standard exponential form?

Answer 13

Hang on let me check something real quick

Answer 14

k

Answer 15

Actually, this is more of a trick question than originally assumed simply because the \(A_o\) part of the exponential function is technically not supposed to change as it represents the initial amount.

Answer 16

I'll have to get back to you on it.

Answer 17

oh really?

Answer 18

Yup, really.

Answer 19

very trick question then, lol

Answer 20

wait a minute

Answer 21

the question is asking "or which of the four operations is the resulting function still a standard exponential model? So technically if I do a vertical dilation by a factor of 3 then it will still be a standard exponential model right?

Answer 22

If you go strictly by that, then I suppose it is. I'm just going to verify it real quick

Answer 23

k

Answer 24

gtg

Answer 25

so i think that both types of dilations keep it in standard exponential form, but not shifts because a horizontal shift would result in b^(x-n) when shifting n units and that isn't in standard exponential form

Answer 26

It asks "Which of the given transformations" and that implies "Which ONE". So if I had to go with one, I'd go with vertical dilation