Answer:
[tex]y =\dfrac{4}{5} x[/tex]
Step-by-step explanation:
From the table, note that for [tex]x\in(0, \infty)[/tex] we have [tex]x> y[/tex], on the other hand for [tex]x\in(-\infty, 0)[/tex] we have [tex]x < y[/tex].
Considering the basic case [tex]x = 0[/tex], we conclude [tex]y = 0 \iff x = 0[/tex], thus [tex]y = x- 2[/tex] is not an option.
Also, once the domain and range have the same signal, [tex]$y =-\frac{5}{4} x$[/tex] can't be an option as well.
Finally, taking [tex]x = 10 \implies y=8[/tex], testing the two remaining cases
[tex]$y =\frac{5}{4} x \implies y=\frac{5}{4} \cdot 10 \implies y = 12.5$[/tex]
[tex]$y =\frac{4}{5} x \implies y=\frac{4}{5} \cdot 10 \implies y=8$[/tex]
The function is [tex]y =\dfrac{4}{5} x[/tex]
