Question

If f ( x ) is a linear function, f ( − 4 ) = − 4 , and f ( 4 ) = − 1 , find an equation for f ( x ) .

Answer 1

Explanation:

linear function

y = ax + b

f(-4) = -4

x = -4

y = -4

-4 = a×-4 + b

f(4) = -1

x = 4

y = -1

-1 = 4a + b

sum both equations

-5 = 0 + 2b

b = -5/2

-1 = 4a - 5/2

3/2 = 4a

a = 3/2 / 4 = 3/8

the function would be

y = 3/8 x - 5/2