Functions that Describe Situations
Key Questions

Suppose we were asked to find the volume of a balloon
we will use the function of volume for a balloon
#v(ballon)=# 4/3 pi r^3##we know radius is 3
#4/3 *pi 3^3# #4 pi* 9# #36pi# Hence there several functions which are much more complex than this.

Consider a taxi and the fare you have to pay to go from A street to B avenue and call it
#f# .#f# will depend upon various things but to make our life easier let assume that depends only upon the distance#d# (in km).
So yo can write that "fare depends upon distance" or in mathlanguage:#f(d)# .A strange thing is that when you sit in the taxy the meter already shows a certain amount to pay...this is à fixed amount you have to pay no matter the distance, let's say,
#2$# .
Now for each km travelled the taxi driver has to pay petrol, maintenance of the vehicle, taxes and get money for himself...so he will charge#1.5$# for each km.
The meter of the taxi will now use the following function to evaluate the fare:
#f(d)=1.5d+2#
This is called "linear" function and allows you to "predict" your fare for each distance travelled (even if#d=0# , i.e., when you only sit in the taxi!)
Now, let us assume that the distance#d# between A street and B avenue is#d=10 km# , you fare wiĺ be:
#f(10)=1.5×10+2=17$# You can now improve your function including additional costs and dependences or build new relationships.
Questions
Expressions, Equations, and Functions

Variable Expressions

Expressions with One or More Variables

PEMDAS

Algebra Expressions with Fraction Bars

Patterns and Expressions

Words that Describe Patterns

Equations that Describe Patterns

Inequalities that Describe Patterns

Function Notation

Domain and Range of a Function

Functions that Describe Situations

Functions on a Cartesian Plane

Vertical Line Test

ProblemSolving Models

Trends in Data