What is the difference between the 'A' value and the 'a' value in the exponential function general formula of f(x)=Aa^x?

Question

What do the two different variables do the a graph of the function?

3462 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-19T18:02:47

$" "$
Please read thee explanation.

$" "$
The general form of an exponential function is given by:

$color(red)(y=f(x)=A(a)^x+C$ , where

$color(blue)(A!=0$ , $color(blue)(a>0$ and $color(blue)(a!=1$ and $color(blue)(x in RR$ and $color(blue)(C$ a constant .

$color(red)(A$ and $color(red)(a$ are two parameters responsible for all stretches, shifts and transformations in the graph of f(x).

Referring to the general form above,

$color(red)(A$ controls the y-intercept of the function $color(red)(f(x).$

$color(red)(a$ is the base of the function $color(red)(f(x).$

We observe that both the parameters $color(red)(A$ and $color(red)a$ control the behavior of the exponential function.

Let us look at the graphs below to understand the behavior of some of the exponential functions:

Graph-1

For this graph, $color(red)(A=1, a=2, C=0$

enter image source here

Graph-2

For this graph, $color(red)(A=2, a=2, C=1$

enter image source here

Graph-3

For this graph, $color(red)(A=1, a=0.5, C=0$

enter image source here

Graph-4

For this graph, $color(red)(A=-1, a=2, C=0$

enter image source here

Hope this helps.