. Anna gets paid $8.75/hour working as a barista at Coffee Break. Her boss pays her
$9.00/hour for creating the weekly advertisement signs. She works a total of 25
hours each week.
a. Let x represent the hours that Anna works each week as a barista.

Write a function ℎ(x) to represent the amount of money that Anna earns working as
a barista.

b. Write a function, f(x) to represent the hours Anna works creating the signs.

c. Let s represent the number of hours that Anna works creating the signs.
Create a function g(s) to represent the money Anna earns creating the signs.

d. Find g( f(x) ). What does this composite function represent?

e. What functions could be combined to represent Anna’s total earnings?
Combine the functions to write an expression that can be used to represent
Anna’s total earnings, where x represents the number of hours she works as a
barista

Let 'x' represent the number of hours that she works as a barista, then [tex]25-x[/tex] would represent the number of hours she works to create signs.

A. We need to write a function h(x) that represents the amount of money that Anna earns working as a barista.

Since she is earning $8.75 per hour and she works as a barista for 'x' hours a week so the function is:

[tex]h(x)=8.75\times x=8.75x[/tex]

[tex]h(x)=8.75x[/tex]

B. We need to write a function f(x) to represent the hours Anna works creating the signs.

Since, in total she works for 25 hours a week so the function to represent the number of hours she work to create signs can be given by:

[tex]f(x)=(25-x)[/tex]

C. If 's' represents the number of hours that Anna works creating signs, we need to create a function g(s) that represents her earning creating signs.

So the number of hours Anna works creating signs for the coffee break is [tex]s[/tex], she gets paid $9.00 an hour for creating signs, so:

[tex]g(s)=9\times s=9s[/tex]

[tex]g(s)=9s[/tex]

D. We need to finf a composite function [tex]g(f(x))[/tex], to find the desired function we need to plug value of f(x) in the function g(s):

[tex]g(f(x))=9s=9(f(x))=9(25-x)=225-9x[/tex]

[tex]g(f(x))=225-9x[/tex]

The composite function g(f(x)) represents Anna's earnings while working just to create signs for the Coffee break.

E. To represent Anna's total earnings the functions that can be combined are h(x) and g(f(x)) because h(x) represents Anna's earnings while working as a barista and g(f(x)) represents Anna's earnings while she creates signs for the coffee break.

The function to represent Anna's total earnings can be given as:

[tex]T(x)=h(x)+g(f(x))=8.50x+225-9x[/tex]

where we must keep in mind that 'x' represents the number of hours she spent working as a barista in a 'week'.