13. Nine days ago, the gas tank on Sue's car was filled with 24 gallons of gasoline. Today there are 6 gallons of gasoline. a. What integer represents the change of gasoline in the past seven days? b. What is the change in gasoline in gallons per day (if she used the same amount every day)?

Step-by-step explanation:

13. Nine days ago, the gas tank on Sue's car was filled with 24 gallons of gasoline. Today there are 6 gallons of gasoline.

a. What integer represents the change of gasoline in the past seven days?

b. What is the change in gasoline in gallons per day (if she used the same amount every day)?

Gasoline difference = 24 - 6 gallons

= 18 gallons

9 days = 6 gallons

1 day = x gallons

=

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!