The equation for the graph of y = -f(x) is [tex]y = -|x + 2| +2[/tex] {x < 0}
The function of the graph is given as:
[tex]y = f(x)[/tex]
The equation of the graph is an absolute value function
An absolute value function is represented as:
[tex]y = a|x - h| + k[/tex]
Where:
[tex]Vertex = (h,k)[/tex]
From the graph, the vertex is at (-2,-2).
So [tex]y = a|x - h| + k[/tex] becomes
[tex]y = a|x + 2| -2[/tex]
A point on the graph is (-4,0).
So, we have:
[tex]0 = a|-4 + 2| -2[/tex]
Simplify
[tex]0 = a|-2| -2[/tex]
Add 2 to both sides
[tex]2 = a|-2|[/tex]
Remove absolute bracket
[tex]2 = 2a[/tex]
Divide both sides by 2
[tex]1 = a[/tex]
Rewrite as:
[tex]a = 1[/tex]
So, we have:
[tex]y = a|x + 2| -2[/tex]
[tex]y = |x + 2| -2[/tex]
The graph stops at x = 0.
So, the function of the graph is [tex]y = |x + 2| -2[/tex] {x < 0}
To draw the graph of y = -f(x), we simply transform f(x) as follows:
[tex](x,y) \to (x,-y)[/tex]
So, the equation for the graph of y = -f(x) is
[tex]y = -|x + 2| +2[/tex] {x < 0}
See attachment for the graph of y = -f(x)
Read more about absolute value functions at:
https://brainly.com/question/3381225
