Respuesta :
The negative before the 2 reflects over the x axis, The +4 shifts the graph 4 units left and the final - 2 shifts it 2 units down.
Its the first choice.
Its the first choice.
Answer:
The correct option is A) shift 4 units left, reflect over the x-axis, shift 2 units down.
Step-by-step explanation:
Consider the provided information
The parent function for the provided function is [tex]f(x)=2^x[/tex] and we need to find the transformations that gives [tex]g(x)=-(2)^{x+4}-2 [/tex] from the parent function.
The rules for transformation are:
[tex]f(x)+c[/tex] Graph shifted upwards by c units.
[tex]f(x)-c[/tex] Graph shifted downwards by c units.
[tex]f(x-c)[/tex] Graph shifted to right by c units.
[tex]f(x+c)[/tex] Graph shifted to left by c units.
[tex]f(-x)=f(x)[/tex] Graph reflected across y-axis.
[tex]f(-x)=-f(x)[/tex] Graph reflected across x-axis.
Now consider the given function [tex]g(x)=-(2)^{x+4}-2 [/tex] replace x with -x [tex]g(x)=-(2)^{-x+4}-2 [/tex]
which shows the function reflected across x-axis.
Now observe the parents function and provided function f(x) and g(x),we can observe the transformations:
The parent function [tex]f(x)=2^x[/tex] is shifted to left by 4 units. From the above rule.
The parent function [tex]f(x)=2^x[/tex] is shifted downwards by 2 units. Because of -2
Hence, the correct option is A) shift 4 units left, reflect over the x-axis, shift 2 units down.
