Final answer:
To write a linear function f with the given values f(0) = 4 and f(1) = -4, the linear function f(x) = -8x + 4 can be used.
Step-by-step explanation:
To write a linear function f with the given values f(0) = 4 and f(1) = -4, we can use the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
First, we find the slope (m) using the given points:
m = (y2 - y1) / (x2 - x1) = (-4 - 4) / (1 - 0) = -8 / 1 = -8
Next, we substitute one of the points into the equation to solve for b:
-4 = -8(1) + b
-4 = -8 + b
b = -4 + 8 = 4
Therefore, the linear function f is f(x) = -8x + 4.