Answer: The first option is correct.
Explanation:
The given piecewise function is,
[tex]y=\begin{cases}-\frac{4}{5}x-3 & \text{ if } x<0\\3x-10 & \text{ if } x\geq2 \end{cases}[/tex]
From the piecewise function we can say that if x<0, then
[tex]f(x)=-\frac{4}{5}x-3[/tex]
If [tex]x\geq2[/tex], then
[tex]f(x)=3x-10[/tex]
Since the f(x) is defined for x<0 and [tex]x\geq2[/tex], therefore the function f(x) is not defined for [tex]0\leq x<2[/tex].
In the graph 2, 3 and 4 for each value of x there exist a unique value of y, therefore the function is defined for all values of x, which is not true according to the given piecewise function.
Only in figure the value of y not exist when x lies between 0 to 2, including 0. It means the function is not defined for [tex]0\leq x<2[/tex], hence the first option is correct.
