Answer:OPTION DStep-by-step explanation:We have to determine which option determines the function given above.To determine the function, just substitute the values and compare LHS and RHS. we have [tex]$ f(4) = 18 $[/tex][tex]$ f(-2) = -12 $[/tex][tex]$ f(0) = -2 $[/tex][tex]$ f(-3) = -17 $[/tex]Here, [tex]$ x $[/tex] is the domain and [tex]$ f(x) $[/tex] is the co-doamin.Therefore, [tex]$ x = \{4, -2, 0, -3\} $[/tex]Now, OPTION A: [tex]$ f(x) = 2x - 5 $[/tex]Substitute x = 4. We get f(x) = 3 [tex]$ \ne $[/tex] 18.So, OPTION A is rejected.Similarly, OPTION B: [tex]$ f(x) = 5x + 2 $[/tex]Substitute x = 4. We get f(4) = 22 [tex]$ \ne $[/tex]18.It is rejected as well.Now, for OPTION C: [tex]$ f(x) = \frac{x}{2} - 5 $[/tex]Substitute x = 4. We get f(4) = -3 [tex]$ \ne $[/tex] 18.So, OPTION C is also rejected.OPTION D: [tex]$ f(x) = 5x - 2 $[/tex]Substitute x = 4. We get f(4) = 18.Substitute the remaining points in domain as well. We notice that it exactly matches the given function. So, OPTION D is the answer.