Question

Which linear function has a greater unit rate, f(x) or g(x)? f(x) = 3.5x + 1 X -2 -10 12 g () -7 -4.5 0.5 3

Answer 1

To determine which linear function has a greater unit rate, we need to calculate the unit rate of each function.

For f(x) = 3.5x + 1:

When x = -2:
f(-2) = 3.5(-2) + 1
f(-2) = -7 + 1
f(-2) = -6

When x = -10:
f(-10) = 3.5(-10) + 1
f(-10) = -35 + 1
f(-10) = -34

When x = 12:
f(12) = 3.5(12) + 1
f(12) = 42 + 1
f(12) = 43

The unit rates for the function f(x) = 3.5x + 1 are as follows:
- When x = -2, unit rate = -3
- When x = -10, unit rate = -3.4
- When x = 12, unit rate = 3.5

For g(x) = 4x - 2:

When x = -7:
g(-7) = 4(-7) - 2
g(-7) = -28 - 2
g(-7) = -30

When x = -4.5:
g(-4.5) = 4(-4.5) - 2
g(-4.5) = -18 - 2
g(-4.5) = -20

When x = 0.5:
g(0.5) = 4(0.5) - 2
g(0.5) = 2 - 2
g(0.5) = 0

When x = 3:
g(3) = 4(3) - 2
g(3) = 12 - 2
g(3) = 10

The unit rates for the function g(x) = 4x - 2 are as follows:
- When x = -7, unit rate = -4
- When x = -4.5, unit rate = -4
- When x = 0.5, unit rate = 4
- When x = 3, unit rate = 4

Therefore, the linear function g(x) = 4x - 2 has a greater unit rate than f(x) = 3.5x + 1.