Functions that Describe Situations
Key Questions
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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.
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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
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Variable Expressions
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Expressions with One or More Variables
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PEMDAS
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Algebra Expressions with Fraction Bars
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Patterns and Expressions
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Words that Describe Patterns
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Equations that Describe Patterns
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Inequalities that Describe Patterns
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Function Notation
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Domain and Range of a Function
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Functions that Describe Situations
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Functions on a Cartesian Plane
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Vertical Line Test
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Problem-Solving Models
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Trends in Data