Function Notation
Key Questions
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An equation is an equality which is satisfied by a unique set of values of your variables. You have, after the
= sign a fixed value, a fixed result.For example: the equation
4x-2=0 has zero as result and onlyx=1/2 as solution; this means that if you substitute the value ofx=1/2 in the equation you have the result zero, i.e., the equation is satisfied.Now, a function is similar, the only difference is that now you can have a lot of results after the
= sign and so you can have a lot of solutions.For example: the function
4x-2=y doesn't have a definite result (as before that was zero) but another variabley , so every time you choose anx you'll get the corresponding value ofy that satisfies it.
If you choose:
x=1 -> y=2
x=2 -> y=6
....etc.If
x=1/2 -> y=0 which is the solution that we found before for our specific equation (in which they was already set as zero)!So to summarize, an equation has a fixed result (after the
= sign) and an unique set of solutions (values of the variables); a function can have a lot of results (possiblyoo ) and, as a consequence, a lot of solutions.hope it helps
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Answer:
I tried this:
Explanation:
Consider a Function ; this is a Rule, a Law that tells us how a number is related to another...(this is very simplified). A function normally relates a chosen value of
x to a determinate value ofy .Consider as an example a vending machine: you put, say
1$ , and you get a can of soda...Our vending machine is relating money and soda. Now you can put the amount you like (
1, 2, 3...$ ) BUT when you put a certain amount the result is only one...I mean if you put1$ you get a soda nothing else...if you want a sandwich you need another amount.The amount of money you put depends upon you while the product is fixed; so the amount of money is INDEPENDENT (you put what you want) the resulting product given by the machine (once you decided) is DEPENDENT upon the amount you put in.
For our mathematical function, once you choose a value for
x the corresponding value ofy DEPENDS upon this choice…Hope I didn't confuse you even more...
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Answer:
You change the
y tof(x) Explanation:
You solve for one variable, typically
y and then change they tof(x) , for example:-10=3x-y becomesf(x)=3x+10
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