Functions and other Graphs

numberandalgebra path adv

Functions and other graphs (Path) | NSW Curriculum Website

• MA5-FNC-P-01 uses function notation to describe and graph functions of one variable and graphs inequalities in one and 2 variables

📖 Prior Knowledge

Content	Prerequisite relationships
Algebraic Techniques	- Substitute values into algebraic expressions → Use function notation f(x) - Expand brackets using the distributive law → Evaluate f(x) at an algebraic argument
Linear Relationships	- Plot points on the Cartesian plane → Define relations and functions
Linear Relationships B	- Graph a line using gradient and intercept → Graph regions for linear inequalities
Indices C	- Determine when square roots are defined → Find the natural domain from an equation
Equations B	- Solve linear inequalities → Graph regions for linear inequalities
Equations C	- Solve quadratic equations by factorisation → Find the natural domain from an equation
Linear Relationships C	- Transform points on the Cartesian plane → Translate graphs of functions
Non-Linear Relationships C	- Graph parabolas and describe transformations → Translate graphs of functions

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 pairs $(x,y)$ 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 notation $f(x)$ when expressing a function
• Use the notation $f(c)$ to determine the value of $f(x)$ when $x=c$

Find the domain and range of a function and graph functions.pdf

• Define the domain as the set of all allowable values of $x$
• Define the range as the set of possible $y$-values as $x$ 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 form $y=f(x)$,  $y=f(x)+c$, $y=f(x-b)$, $y=kf(x)$ and $y=f(ax)$, and describe their transformations

Graph regions corresponding to linear inequalities in one and 2 variables.pdf

• Graph linear inequalities of the form $ax+by>c$, testing whether the points satisfy the given inequality and shading appropriate regions