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h ' (x) = 4 _____is the rate of change on given interval.

The function is linear, so the rate of change is constant. Another word for rate of change is slope.  The slope of the line is 4.

y = mx + b (m is the slope; b is the y-intercept)We can do the math if your teacher wants.

f(x) = 4x -3

f(1) = 4 -3 = 1

f(0) = 0 -3 = -3

slope = (1 -(-3)) / (1-0) = 4/1 = 4