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Which of the following describes the transformations of g (x) = negative (2) Superscript x + 4 Baseline minus 2 from the parent function f (x) = 2 Superscript x?
shift 4 units left, reflect over the x-axis, shift 2 units down
shift 4 units left, reflect over the y-axis, shift 2 units down
shift 4 units right, reflect over the x-axis, shift 2 units down
shift 4 units right, reflect over the y-axis, shift 2 units down

Respuesta :

luisejr77

Answer: First option.

Step-by-step explanation:

Below are some transformations for a function [tex]f(x)[/tex]:

1. If [tex]f(x)+k[/tex], the function is shifted "k" units up.

2 If [tex]f(x)-k[/tex], the function is shifted "k" units down.

3. If [tex]f(x-k)[/tex], the function is shifted "k" units right.

4. If [tex]f(x+k)[/tex], the function is shifted "k" units left.

5. If [tex]-f(x)[/tex], the function is reflected over the x-axis.

6. If [tex]f(-x)[/tex], the function is reflected over the y-axis.

Then, given the parent function [tex]f(x)[/tex]:

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

And knowing that the the other function is:

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

You can identify that the function [tex]g(x)[/tex] is obtained by:

- Shifting the function [tex]f(x)[/tex] 4 units left.

-  Reflecting the function  [tex]f(x)[/tex] 4 over the x-axis.

- Shifting the function [tex]f(x)[/tex] 2 units down.

cactuspoopdogbrid

Answer:

A is correct

Step-by-step explanation:

  • Shift 4 units left, reflect over the x-axis, shift 2 units down