Combining Linear Functions

a

To calculate the population of the two cities combined, we need to add the given functions.

f (x) + g (x)

We can find this sum by substituting the function rules into this equation and simplifying.

f (x) + g (x)

f (x) = 200 x + 25

,

g (x) = 175 x - 15

(200 x + 25) + (175 x - 15)

RemoveParRemove parentheses

200 x + 25 + 175 x - 15

AddSubTermsAdd and subtract terms

375 x + 10

Therefore, the population of these two cities after any years can be modeled by

375 x + 10 .

b

This time we are asked to find the difference in the populations of these two cities. This means we should subtract the given functions.

f (x) - g (x)

Let's evaluate this difference by substituting the function rules into this equation and simplifying.

f (x) - g (x)

f (x) = 200 x + 25

,

g (x) = 175 x - 15

(200 x + 25) - (175 x - 15)

RemoveParRemove parentheses

200 x + 25 - (175 x - 15)

DistrDistribute

(- 1)

200 x + 25 - 175 x + 15

AddSubTermsAdd and subtract terms

25 x + 40

Therefore, we can find the difference in the populations of these cities using the formula

25 x + 40 .

Combining Linear Functions 1.3 - Solution