Question

The parent function f (x)= 2^xis reflected across the x-axis,
then shifted 2 units left and 6 units down. Write an equation
to represent the new function.

Answer 1

Answer:

$F(x) = 2^{x+2} - 6$

Step-by-step explanation:

To shift a function F(x) a units to the left, we do:

$F(x) = F(x+a)$

In this problem, we have that:

$F(x) = 2^{x}$

So, shifting 2 units left:

$F(x) = 2^{x+2}$

Then

To shift a units down, we do:

$F(x) = F(x) - a. So

[tex]F(x) = 2^{x+2}$

Shifting 6 units down

$F(x) = 2^{x+2} - 6$