To write a linear function f(x) with the values f(3) = -4 and f(5) = -4, we can use the point-slope form of a linear equation:
f(x) - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
Using the two given points, we have:
f(3) = -4 and f(5) = -4
This means that (3, -4) and (5, -4) are two points on the line.
To find the slope, we can use the slope formula:
m = (y2 - y1) / (x2 - x1)
m = (-4 - (-4)) / (5 - 3)
m = 0 / 2
m = 0
Therefore, the slope of the line is 0.
Using the point-slope form with the point (3, -4) and the slope m = 0, we get:
f(x) - (-4) = 0(x - 3)
f(x) + 4 = 0
f(x) = -4
So, the linear function f(x) that passes through the points (3, -4) and (5, -4) is f(x) = -4.