Answer: [tex]f(x)=-4x+4[/tex]
Step-by-step explanation:
We know that , the linear function is given by :-
[tex]f(x)=mx+c[/tex] , where m = slope and c is the value of f(x) at x =0. ...(i)
The given values of function f(x) are f (0) =4 ... (ii)and f (3)= -8 ...(iii)
.
From (i) and (ii) , we get c= 4 ...(iv)
From (i) and (iii) , we get [tex]-8=m(3)+c[/tex]
Put value of c from (iv) , we get [tex]-8=3x+4[/tex][tex]\Rightarrow\ 3x=-4-8=-12[/tex]
[tex]\Rightarrow\ x=\dfrac{-12}{3}=-4[/tex]
Put value of c and x in (i) , our required linear function will becomes
[tex]f(x)=-4x+4[/tex]
Hence, the linear function f with the values f (0) =4 and f (3)= -8 are :
[tex]f(x)=-4x+4[/tex]
