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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.

The parent function f x 2xis reflected across the xaxis then shifted 2 units left and 6 units down Write an equation to represent the new function class=

Respuesta :

Answer:

[tex]F(x) = 2^{x+2} - 6[/tex]

Step-by-step explanation:

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

[tex]F(x) = F(x+a)[/tex]

In this problem, we have that:

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

So, shifting 2 units left:

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

Then

To shift a units down, we do:

[tex]F(x) = F(x) - a. So

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

Shifting 6 units down

[tex]F(x) = 2^{x+2} - 6[/tex]

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