Question

Which linear function has a greater unit rate, f(x) or g(x)?
f(x) = 3.5x + 1
x: -2, -1, 0, 1, 2
g(x): -7, -4.5, -2, 0.5, 3

A) f(x)
B) g(x)
C) The unit rates are the same.
D) There is not enough information given to compare the unit rates.

Answer 1

To determine the unit rates for each function, we can find the change in y for each function divided by the change in x.

For f(x):
change in y = f(1) - f(0) = (3.5(1) + 1) - (3.5(0) + 1) = 4.5
change in x = 1
Unit rate for f(x) = change in y / change in x = 4.5 / 1 = 4.5

For g(x):
change in y = g(1) - g(0) = (-7 - 2) - (-2 + 1) = -9
change in x = 1
Unit rate for g(x) = change in y / change in x = -9 / 1 = -9

Since the unit rate for f(x) is 4.5 and the unit rate for g(x) is -9, the greater unit rate is for f(x) (Option A).