Week 13 of Math 10 and Week 2 of online classes. This week we started focusing more on functions and how to express them on a graph and how to interpret them. In this blog post I will be explaining the different ways functions can be shown and how to interpret a graph.
For starters, we can represent functions in three different ways:
- Equations
- Mapping Notation
- Function Notation
Equations are your typical y=x expression. For example, y=3x+4 is a form of a function because it has a degree of 1 making it a linear expression and it does not result in a vertical line which is not a function.
Mapping notation is represented through f:x —–> 3x+4 and this is used as a way to find a specific point rather than give a line. You can find the specific point by plugging in a number into the x value and simplifying. So if f:(-2) then 3(-2)+4=-2 which gives you the specific point and ordered pair of the function as seen here.
Function notation is represented through f(x)=3x+4. Solving this is no different from solving mapping notation, but the difference is that f represents the name of the function, meaning that we can have different functions add or subtract into one another. So if f(x)= 3x+4 and g(x)= 4x-2 and x= 5 we can subtract them.
Next is how to interpret graphs with them. Let’s say we were given a graph that looks like this:
We can find out what the specific point that a function notation gives. If we were given f(7) we can find the point where f(7) and the graph intersect and find the y value, which for this case is 3.
This also applies to finding the x value too. If f(x)=6 then we can estimate that the x value is 4.5 based off the point that 6 intersects with on the graph.
And that’s how function notation works!
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