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

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## 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

In a particular math class, the overall percent grade corresponds to a grade-point average. Is grade-point average a function of the percent grade? Is the percent grade a function of the grade-point average? [link] shows a possible rule for assigning grade points.

 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.

#### Questions & Answers

12, 17, 22.... 25th term
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
sure. what is your question?
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8