Question

Write a linear function f with the values f (0) =4 and f (3)= -8

Answer 1

(0,4) and (3,-8) has segment of slope -8-4 / 3-0 = -12/3 = -4. y intercept is given to us as 4

equation is

y-4=-4(x) in point slope form
y+8=-4(x-3) using the other point
y=-4x+4 in slope intercept form
4x+y=4 in standard form

Answer 2

Answer:
`f(x)=-4x+4`

Explanation:

We know that , the linear function is given by :-

`f(x)=mx+c` , 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
`-8=m(3)+c`

Put value of c from (iv) , we get
`-8=3x+4`
`\Rightarrow\ 3x=-4-8=-12`

`\Rightarrow\ x=(-12)/(3)=-4`

Put value of c and x in (i) , our required linear function will becomes

`f(x)=-4x+4`

Hence, the linear function f with the values f (0) =4 and f (3)= -8 are :

`f(x)=-4x+4`