Question

May someone please give me am example how to solve a transformation of exponential function

Answer 1

When talking about transformating any function we use the graph of the parent function and make the different shiftments there can be done when making a transformation.

When making a shift across the x-axis we will be affecting the value that is input at x, this can be done by adding or substracting and it should look like this

$a^x\Rightarrow a^{(x\pm c)}$

When this transformation is done the function is shifted to the left the addition must be a positive value, so if we wanted to shift a function 2 units to the left we will make this transformation

$a^x\Rightarrow a^{(x+2)}$

In the other hand if the function wanted to be shifted 2 units to the right we would make the following transformation

$a^x\Rightarrow a^{(x-2)}$

The other transformation we can do is move the function along the y axis, this transformation affects the y coordinate, and it can be obtained by adding or substracting values to the function in this way

$a^x\Rightarrow a^x\pm d^{}$

When we want to shift the function up, we add as many units we want to move the function. For example if we wanted to move a funtion 5 units up the transformation that must be done is:

$a^x\Rightarrow a^x+5$

On the contrary if we wanted to move the function 5 units down we should substract instead of adding.

$a^x\Rightarrow a^x-5$

Applying this to the worksheet:

a. The transformation is

$2^x\Rightarrow2^{(x-2)}-6$

According to the information given above the function has vertical and horixontal shiftments.

Since the coordinate x is substracted 2, the function is shifted to units to the right.

Since the function is also being substracted a 6, the function is shifted 6 units down.

The transformation should look like this: