This week in math 10 we finished our relations and functions unit and started to move into our final unit on slopes and linear equations. I believe the most important thing I learned this week was how relations and functions work. This is important to me because once you understand the different tricks on how to determine if an equation or graph are a relation or function it can be very simple.

 

The most important rule for functions is that every input has only ONE output value.

For example the coordinates listed below are functions because every input value(underlined coordinates) have different output variables.

The table value below is a relation because one of the input variables is repeated except they have different output variables.

A trick to tell if graphs are relations or functions is by using a pencil and glide it along the graph vertically. If there are more than one point along the same vertical line it is a relation because that means the input has more than one output.

The graph above is a function because each input has one output.

The graph above is a relation because certain inputs have more than one output.

Function Notation:

Equation- f(x)= 3x+2

When you are given f(2) it means that the (x)=2

The first step is to take the 2 and put it in place of the x.

3(2)+2

Once this is done you can solve the equation.

3(2)+2

6+2=8

So f(2)=8

 

Equation- f(x)=3x-4. Determine what the value of x, if f(x)=11

The first step is to take the equation and have it equal 11.

3x-4=11

Once you create the new equation you can solve for x.

3x-4=11

3x=11+4

3x=15

x=5

When f(x)=11 x=5