Answer:
[tex]f(x)=\left \{ {{x^2+4}\ \ \ \ \ x<2 \atop {-x+4}\ \ \ x\geq 2}\right[/tex]
C is correct
Step-by-step explanation:
In the given graph function break at point x=2.
Left side about point x=2 is parabolic and right side straight line.
So, it would be piece wise function.
For parabola:
vertex: (0,4) and passing point (2,8)
[tex]y=a(x-h)^2+k[/tex]
[tex]y=ax^2+4[/tex]
[tex]a=1[/tex]
[tex]y=x^2+4[/tex] For x<2
For straight line:
Twp points (4,0) and (2,2)
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-2=\dfrac{0-2}{4-2}(x-2)[/tex]
[tex]y-2=-1(x-2)[/tex]
[tex]y=-x+4[/tex] For x≥2
Hence, The piece wise function will be
[tex]f(x)=\left \{ {{x^2+4}\ \ \ \ \ x<2 \atop {-x+4}\ \ \ x\geq 2}\right[/tex]
