Answer:
A. [tex]f(x)=-4|x+2|+3[/tex]
Step-by-step explanation:
We have been given an image of an absolute function. We are asked to find the formula for our given absolute function.
The formula of parent absolute function is [tex]f(x)=|x|[/tex] with vertex at (0,0)
We can see that the vertex of our given function is at [tex](-2,3)[/tex]. This means that our function is shifted to left by 2 units. We can represent this information as: [tex]f(x)=|x--2|=|x+2|[/tex]
We can also see that our graph is reflected across x-axis, so after reflection our function would be [tex]f(x)=-|x+2|[/tex]
We can see that our graph is shifted upwards by 3 units, so graph after shifting would be [tex]f(x)=-|x+2|+3[/tex].
Our graph is stretched vertically by a scale factor of 4, so after stretching our function would be [tex]f(x)=-4|x+2|+3[/tex].
Therefore, option A is the correct choice.
