Question

A function, f, is represented by an equation and a linear function, g, is represented by a table of values.

f(x)=9x−18
x -3 2 5
g(x) -48 -8 16


Which statement is true about the rates of change of the two functions?



(1 point)
Responses

f(x) has a greater rate of change.
f(x) has a greater rate of change.

g(x) has a greater rate of change.
g(x) has a greater rate of change.

The two functions have equal rates of change.
The two functions have equal rates of change.

There is not enough information given to determine each function's rate of change.

Answer 1

f(x) has a greater rate of change.

We can determine the rate of change of a linear function by finding the slope, which is the coefficient of x in the equation. In this case, f(x) = 9x - 18, so the rate of change is 9.

For the function g(x) represented by the table, we can calculate the rate of change by finding the difference in the function values and dividing by the difference in the input values.

For x = -3 and x = 2, the rate of change is (-8 - (-48)) / (2 - (-3)) = 40 / 5 = 8.
For x = 2 and x = 5, the rate of change is (16 - (-8)) / (5 - 2) = 24 / 3 = 8.

Since both intervals have a rate of change of 8, which is less than the rate of change of f(x) which is 9, f(x) has a greater rate of change than g(x).