Answer:
Piecewise function:
[tex]f(x)=\left\{\begin{matrix}2x &\ \ \ \text{ if }-3\leq x<0\\3&\ \ \ \text{ if }\frac{1}{2}<x<\frac{3}{2}\end{matrix}\right.[/tex]
Step-by-step explanation:
Given: Piece wise function graph.
We need to find the function.
In graph we can see two piece
For -3≤x≤0
End points on graph (-3,-6) and (0,0)
[tex]y-0=\dfrac{6}{3}(x-0)[/tex]
[tex]y=2x[/tex]
[tex]\text{For } \dfrac{1}{2}<x<\dfrac{3}{2}[/tex]
It is horizontal line. The equation of horizontal line is y=k.
Equation: y=3
Now, we write as piecewise function.
[tex]f(x)=\left\{\begin{matrix}2x &\ \ \ \text{ if }-3\leq x<0\\3&\ \ \ \text{ if }\frac{1}{2}<x<\frac{3}{2}\end{matrix}\right.[/tex]
First blank = 2x
Second Blank = 3
