Respuesta :

Answer:

Shift 4 units left, reflected over x-axis, shift two units down.

Step-by-step explanation:

We have been given formula of a parent function [tex]f(x)=2^x[/tex] and we are asked to find the transformations that are used to get [tex]g(x)=-(2)^{x+4}-2[/tex] from our given parent function.

Let us recall transformation rules.

[tex]f(x-a)\rightarrow \text{Graph shifted to right by a units}[/tex],

[tex]f(x+a)\rightarrow \text{Graph shifted to left by a units}[/tex],

[tex]f(x)+a\rightarrow \text{Graph shifted upwards by a units}[/tex],

[tex]f(x)-a\rightarrow \text{Graph shifted downwards by a units}[/tex],

[tex]f(-x)\rightarrow \text{Graph reflected across y-axis}[/tex],

[tex]-f(x)\rightarrow \text{Graph reflected across x-axis}[/tex].

Upon looking at our given f(x) and g(x),we can see these transformations:

  • Our parent function is shifted to left by 4 units.
  • Our parent function is reflected over x-axis.
  • Our parent is shifted downwards by 2 units.

Therefore, option A is the correct choice.

MrRoyal

The transformation from f(x) to g(x) is (a) shift 4 units left, reflect over the x-axis, shift 2 units down

The parent function of a square root function is represented as:

[tex]f(x) =2^x\\[/tex]

When the function is shifted 4 units left, we have the following equation

[tex]f'(x) =2^{x+4}[/tex]

When the function is reflected over the x-axis, we have the following equation

[tex]f"(x) =-2^{x+4}[/tex]

When the function is shifted 2 units down, we have the following equation

[tex]f"(x) =-2^{x+4} - 2[/tex]

So, we have:

[tex]g(x) =-2^{x+4} - 2[/tex]

Hence, the transformation from f(x) to g(x) is (a)

Read more about function transformation at:

https://brainly.com/question/4057530

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