Answer: [tex]f(x)=\begin{cases} x^2 +4, x < 3 \\ -x+4, x \geq 3 \end{cases}[/tex]
Step-by-step explanation:
By inspection, we know the equation of the parabola is [tex]y=x^2 +4[/tex] and the equation of the line is [tex]y=-x+4[/tex].
Since there is an open hole at x=3 for the parabola and a closed hole at x=3 for the line, the function is
[tex]f(x)=\begin{cases} x^2 +4, x < 3 \\ -x+4, x \geq 3 \end{cases}[/tex]
