Question

The function f(x) = 15x + 420 can be used to model a store's inventory of devices in one month. The function g(x) = 18x + 380 can be used to model a store's inventory of devices the second month. Write a new function in function notation, using h(x), to model the store's total inventory for both months.

Answer 1

The function h(x) that models the store's total inventory for both months is h(x) = 33x + 800, obtained by summing the first and second month's inventory models.

Step-by-step explanation:

To model the store's total inventory for the first and second months, we need to find the sum of the inventory functions for each month. These functions are given as f(x) = 15x + 420 for the first month and g(x) = 18x + 380 for the second month. The new function, h(x), is found by adding the two functions together:

h(x) = f(x) + g(x)

h(x) = (15x + 420) + (18x + 380)

To combine them, we simply add the following terms:

h(x) = 15x + 18x + 420 + 380

h(x) = 33x + 800

So, h(x) = 33x + 800 is the function that models the store's total inventory over the two-month period.

The new function h(x) effectively models the store's total inventory over the two months, providing a consolidated representation that incorporates both the first-month inventory function f(x) and the second-month inventory function g(x). This allows for a comprehensive analysis of the store's overall inventory trend over the specified time period.