Respuesta :
That would be option A . Note its shifted left 3 not 6 because we have 2x in the parentheses ( 2x + 6) = 2(x + 3)
Answer:
A. The graph is compressed horizontally by a factor of 2, shifted left 3, reflected over the x-axis, and translated up 3.
Step-by-step explanation:
We have been given graph of a function [tex]y=-(2x+6)^2+3[/tex]. We are asked to compare the graph to the parent function.
Let us recall transformation rules:
Reflection:
[tex]f(x)=-f(x)\Rightarrow\text{Graph reflected about x-axis}[/tex],
[tex]f(x)=f(-x)\Rightarrow\text{Graph reflected about y-axis}[/tex]
Upon looking at our given function, we can see that graph is reflected about x-axis.
Translation:
[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 downwards by a units}[/tex],
[tex]f(x)+a\Rightarrow\text{Graph shifted upwards by a units}[/tex].
[tex]y=-(2(x+3))^2+3[/tex]
Stretch:
[tex]f(x)=f(ax);a>1\Rightarrow\text{Function compressed horizontally}[/tex]
We can see that graph is shifted to left 3 units and upwards by 3 units.
Therefore, option A is the correct choice.
