# 3.1 Functions and function notation  (Page 2/21)

 Page 2 / 21

## Determining if menu price lists are functions

The coffee shop menu, shown in [link] consists of items and their prices.

1. Is price a function of the item?
2. Is the item a function of the price?
1. Let’s begin by considering the input as the items on the menu. The output values are then the prices.

Each item on the menu has only one price, so the price is a function of the item.

2. Two items on the menu have the same price. If we consider the prices to be the input values and the items to be the output, then the same input value could have more than one output associated with it. See [link] .

Therefore, the item is a not a function of price.

## Determining if class grade rules are functions

 Percent grade 0–56 57–61 62–66 67–71 72–77 78–86 87–91 92–100 Grade-point average 0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0

For any percent grade earned, there is an associated grade-point average, so the grade-point average is a function of the percent grade. In other words, if we input the percent grade, the output is a specific grade point average.

In the grading system given, there is a range of percent grades that correspond to the same grade-point average. For example, students who receive a grade point average of 3.0 could have a variety of percent grades ranging from 78 all the way to 86. Thus, percent grade is not a function of grade-point average.

[link] http://www.baseball-almanac.com/legendary/lisn100.shtml. Accessed 3/24/2014. lists the five greatest baseball players of all time in order of rank.

Player Rank
Babe Ruth 1
Willie Mays 2
Ty Cobb 3
Walter Johnson 4
Hank Aaron 5

1. Is the rank a function of the player name?
2. Is the player name a function of the rank?

a. yes; b. yes. (Note: If two players had been tied for, say, 4th place, then the name would not have been a function of rank.)

## Using function notation

Once we determine that a relationship is a function, we need to display and define the functional relationships so that we can understand and use them, and sometimes also so that we can program them into graphing calculators and computers. There are various ways of representing functions. A standard function notation is one representation that facilitates working with functions.

To represent “height is a function of age,” we start by identifying the descriptive variables $h$ for height and $a$ for age. The letters $\text{\hspace{0.17em}}f,\text{\hspace{0.17em}}g,$ and $\text{\hspace{0.17em}}h\text{\hspace{0.17em}}$ are often used to represent functions just as we use $x,\text{\hspace{0.17em}}y,$ and $z$ to represent numbers and $A,\text{\hspace{0.17em}}B,$ and $C$ to represent sets.

Remember, we can use any letter to name the function; the notation $\text{\hspace{0.17em}}h\left(a\right)\text{\hspace{0.17em}}$ shows us that $\text{\hspace{0.17em}}h\text{\hspace{0.17em}}$ depends on $\text{\hspace{0.17em}}a.\text{\hspace{0.17em}}$ The value $\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ must be put into the function $\text{\hspace{0.17em}}h\text{\hspace{0.17em}}$ to get a result. The parentheses indicate that age is input into the function; they do not indicate multiplication.

what are you up to?
nothing up todat yet
Miranda
hi
jai
hello
jai
Miranda Drice
jai
aap konsi country se ho
jai
which language is that
Miranda
I am living in india
jai
good
Miranda
what is the formula for calculating algebraic
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
Miranda
state and prove Cayley hamilton therom
hello
Propessor
hi
Miranda
the Cayley hamilton Theorem state if A is a square matrix and if f(x) is its characterics polynomial then f(x)=0 in another ways evey square matrix is a root of its chatacteristics polynomial.
Miranda
hi
jai
hi Miranda
jai
thanks
Propessor
welcome
jai
What is algebra
algebra is a branch of the mathematics to calculate expressions follow.
Miranda
Miranda Drice would you mind teaching me mathematics? I think you are really good at math. I'm not good at it. In fact I hate it. 😅😅😅
Jeffrey
lolll who told you I'm good at it
Miranda
something seems to wispher me to my ear that u are good at it. lol
Jeffrey
lolllll if you say so
Miranda
but seriously, Im really bad at math. And I hate it. But you see, I downloaded this app two months ago hoping to master it.
Jeffrey
which grade are you in though
Miranda
oh woww I understand
Miranda
Jeffrey
Jeffrey
Miranda
how come you finished in college and you don't like math though
Miranda
gotta practice, holmie
Steve
if you never use it you won't be able to appreciate it
Steve
I don't know why. But Im trying to like it.
Jeffrey
yes steve. you're right
Jeffrey
so you better
Miranda
what is the solution of the given equation?
which equation
Miranda
I dont know. lol
Jeffrey
Miranda
Jeffrey
answer and questions in exercise 11.2 sums
how do u calculate inequality of irrational number?
Alaba
give me an example
Chris
and I will walk you through it
Chris
cos (-z)= cos z .
what is a algebra
(x+x)3=?
6x
Obed
what is the identity of 1-cos²5x equal to?
__john __05
Kishu
Hi
Abdel
hi
Ye
hi
Nokwanda
C'est comment
Abdel
Hi
Amanda
hello
SORIE
Hiiii
Chinni
hello
Ranjay
hi
ANSHU
hiiii
Chinni
h r u friends
Chinni
yes
Hassan
so is their any Genius in mathematics here let chat guys and get to know each other's
SORIE
I speak French
Abdel
okay no problem since we gather here and get to know each other
SORIE
hi im stupid at math and just wanna join here
Yaona
lol nahhh none of us here are stupid it's just that we have Fast, Medium, and slow learner bro but we all going to work things out together
SORIE
it's 12
what is the function of sine with respect of cosine , graphically
tangent bruh
Steve
cosx.cos2x.cos4x.cos8x
sinx sin2x is linearly dependent
what is a reciprocal
The reciprocal of a number is 1 divided by a number. eg the reciprocal of 10 is 1/10 which is 0.1
Shemmy
Reciprocal is a pair of numbers that, when multiplied together, equal to 1. Example; the reciprocal of 3 is ⅓, because 3 multiplied by ⅓ is equal to 1
Jeza
each term in a sequence below is five times the previous term what is the eighth term in the sequence
I don't understand how radicals works pls
How look for the general solution of a trig function