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.