Question

Function f is a linear function with an initial value of 17 and a rate of change of –3. Some values for the linear function g are shown in the table below. By how much does g exceed f when x = 5?

x 0 1 2 3
g(x) -8 -4 0 4

when x = 5, g exceeds f by ________

Answer 1

Based on the given linear function with initial value of 17 and a rate of change of -3, When x = 5, g exceeds f by 10 .

How to calculate value of g

To find out how much g exceeds f when x = 5, determine the values of f and g at x = 5 and then calculate the difference between them.

The linear function f has an initial value of 17 and a rate of change of -3. This means that for each unit increase in x, the value of f decreases by 3. Therefore, express f as:

f(x) = 17 - 3x

Now, calculate the value of f when x = 5:

f(5) = 17 - 3(5)

= 17 - 15

= 2

The table provides the values of g for x = 0, 1, 2, and 3.

To find the value of g at x = 5, observe the pattern in the table. It can be observed that for each unit increase in x, the value of g increases by 4. Therefore, express g as:

g(x) = -8 + 4x

Now, calculate the value of g when x = 5:

g(5) = -8 + 4(5)

= -8 + 20

= 12

To determine how much g exceeds f when x = 5, calculate the difference between the values of g and f:

g(5) - f(5) = 12 - 2

= 10

Therefore, g exceeds f by 10 when x = 5.