#NumberAndAlgebra #Path #Adv
>[!info]- [Functions and other graphs (Path) | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/content/stage-5/fa4ba33ef2)
>- MA5-FNC-P-01 uses function notation to describe and graph functions of one variable and graphs inequalities in one and 2 variables
## š Prior Knowledge
| Content | Prior knowledge | Used for |
| ------------------------------ | --------------------------------------------------------------------- | --------------------------------------------- |
| [[Equations B]] | - inequalties | - finding natural domain |
| [[Equations C]] | - solving complex equations | - finding intercepts |
| [[Linear Relationships C]] | - graphing straight lines | - graphing linear inequalities in 2 variables |
| [[Non-Linear Relationships C]] | - transformations of parabolas, hyperbolas, exponentials, hyperbolas. | - transformations of any function |
## [[Define relations and functions, and use function notation.pdf]]
- Define a relation over 2 sets as an association between the elements of one set to the elements of another set
- Notate relations as a set of ordered pairsĀ $(x,y)$Ā of real numbers
- Define a function as a relation over 2 sets where each element of the first set is associated with exactly one element in the second set
- Apply the vertical line test on a graph to decide whether it represents a function
- Use the notationĀ $f(x)$Ā when expressing a function
- Use the notationĀ $f(c)$Ā to determine the value ofĀ $f(x)$Ā whenĀ $x=c$
## [[Find the domain and range of a function and graph functions.pdf]]
- Define the domain as the set of all allowable values ofĀ $x$
- Define the range as the set of possibleĀ $y$-values asĀ $x$Ā varies over the domain of the function
- Determine and describe the domain and range for a variety of functions
- Use graphing applications to graph and compare functions of the formĀ $y=f(x)$,Ā Ā $y=f(x)+c$,Ā $y=f(x-b)$,Ā $y=kf(x)$Ā andĀ $y=f(ax)$, and describe their transformations
## [[Graph regions corresponding to linear inequalities in one and 2 variables.pdf]]
- Graph linear inequalities of the formĀ $ax+by>c$, testing whether the points satisfy the given inequality and shading appropriate regions