Question

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

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

Answer 1

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Please read thee explanation.

Explanation:

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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`

Graph-2

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

Graph-3

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

Graph-4

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

Hope this helps.