Final answer:
To write the linear function with the given values f(-2)=6 and f(0)=-4, calculate the slope using the formula (change in y)/(change in x) to find the slope of -5, and use the y-intercept of -4. Thus, the linear function is F(x) = -5x - 4.
Step-by-step explanation:
To write the linear function f(x) with the given values f(-2)=6 and f(0)=-4, we need to find the slope and y-intercept of the line. We can use the formula for the slope (m) given by:
m = (y2 - y1)/(x2 - x1)
Using the given points (-2, 6) and (0, -4), we can find the slope:
m = (-4 - 6)/(0 - (-2))
m = (-10)/2
m = -5
The y-intercept (b) is the value of f(x) when x=0, which is given as -4. Therefore, b = -4.
The linear equation is of the form y = mx + b, so it becomes:
f(x) = -5x - 4
So the correct function is B. F(x) = -5x - 4.