Question

What effect will introducing a constant have on an exponential function?

Answer 1

Take y=x^2 and y=5x^2
they are both parabolas centered at (1,0) (y=0^2 and y=5(0^2)
but if you compare the first move of x to find y, you'll notice something
y=1^2 == 1
y=5(1^2) == 5
if you continue this, you will notice that the growth (in this case I mean slope) of the one with the constant is much faster, so graphically, it makes the parabola wider.

Answer 2

I meant, the are centered at (0,0)...

Answer 3

so basically it increases right

Answer 4

It depends on what you mean by "introducing a constant."

You could be multiplying by a scalar \(k\) so that you have \(f(x)\to kf(x)\), which is what @agreene is talking about.

Or perhaps you mean to multiply the argument/input of the function by a scalar, such that you have \(f(x)\to f(kx)\), which isn't quite the same as the first.

Or you could also mean to add a constant, \(f(x)\to f(x)+k\).

Or you could be adding the constant to the input, \(f(x)\to f(x+k)\).

Can you be more specific?

Answer 5

it was just a general question it does not specify anything in particular but i will make sure to take not on what you said too. thank you!

Answer 6

np