Question

Graph problem
If we want to shift the graph to the left, we would write the equation y=f(x) into y=f(x+k), where k is a positive value. What about if I want to shift the graph of y=e^[f(x)] by k units to the left. What should I do? Should I do it in the normal way?

Answer 1

y=e^[f(x)]?

Answer 2

Yes.. If I want to shift this graph by k units to the left

Answer 3

What's f(x)? Just a general function?

Answer 4

Yes

Answer 5

Well, same thing.

Answer 6

Really?!

Answer 7

Wait.

Answer 8

say f(x)=x

Answer 9

Let me test this out with geogebra.

Answer 10

Yup.

Answer 11

Assuming f(x) is a function of x, ou basically have f(x+k)

Answer 12

So the graph would be y=e^[f(x+k)]?

Answer 13

Yes

Answer 14

if f(x)=e^x, you have e^(e^(x+k))

Answer 15

Wow~ that's weird!!!
so, y = f(x) = e^[f(x)]
= f(x+k) = e^ (e^(x+k)) ??

Answer 16

Think about it. For any function f(x), if you add a number k to every x, then f(x) needs k less input to get output f1(x).

Answer 17

If you subtract k from every input x, however, then f(x) needs k more input to get output f2(x). thus for the former case the graph is shifted left, and for the latter case the graph is shifted right, because it requires less to be larger (in the case of e^x, all other functions work, monotonic or not) and because it requires more to be larger (also in the case of e^x), respectively.

Answer 18

If you have a polynomial, say x^3-x^2+2x=f(x), f(x+k) would be (x+3)^3-(x+3)^2+2(x+3)

Answer 19

I think I understand the general case. Was not sure when the power is the function one..