Question

given the functions f (x) = 2x − 5 and g(x), represented in the table, which function has a greater rate of change?

x	2	4	6
g(x)	5	11	17

options:

• f (x) has a greater rate of change
• the rate of change for f (x) is equal to the rate of change of g (x)
• g(x) has a greater rate of change
• the rate of change of g(x) is undefined

Explanation:

Step1: Find the rate of change of \( f(x) \)

For a linear function \( y = mx + b \), the rate of change is \( m \).
For \( f(x)=2x - 5 \), the rate of change \( m_f=2 \).

Step2: Find the rate of change of \( g(x) \)

The rate of change formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Using the points \((x_1 = 2,y_1 = 5)\) and \((x_2 = 4,y_2 = 11)\) from the table:
\( m_g=\frac{11 - 5}{4 - 2}=\frac{6}{2}=3 \).

Answer:

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