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.
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.
Answers
GPT 3.5
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).
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).