- Mathematics Advanced
- Year 11
Functions and Relations
approx. 14 hrs
12 topics
46 concepts
Become proficient in Functions and Relations to enhance your performance in Mathematics in the HSC.
approx. 14 hrs
12 topics
46 concepts
Become proficient in Functions and Relations to enhance your performance in Mathematics in the HSC.
The content covered in Year 11 Functions and Relations is aligned with the NSW Mathematics syllabus. In Functions and Relations, students learn the concept of a function and a relation, and the relationship between a function and its graph. We help students demonstrate competence in sketching a graph by identifying its type, using the known properties and observing where the function increases or decreases, its symmetrical properties, domain, range and any points of discontinuity.
This learning program is made up of the following 12 topics, broken down into 46 concepts.
Determine if a function is one-to-one
Even and odd functions
Identify if a set of coordinates is a function
Use function notation to find the output of a single function
Use the vertical line test on a graph to decide whether it represents a function
Finding the output of a piecewise defined function
Range of absolute value functions
Domain of absolute value functions
Range of a single function
Domain of a single function
Sketch a cubic function applying reflection of the graph across the x or y axis
Sketch a cubic function with dilation
Sketch a cubic function applying vertical translation of the graph
Sketch a cubic function applying horizontal translation of the graph
Sketching cubics
Sketch a power function with dilation
Sketch a power function applying horizontal translation of the graph
Sketch a power function applying vertical translation of the graph
Sketch a power function applying reflection of the graph across the x or y axis
Sketching graphs with a higher-order power of four or more
Finding points of intersection of a line with a hyperbola
Sketch a hyperbola applying horizontal translation of the graph
Determine the equations of asymptotes
Sketch a hyperbola with dilation
Sketch a hyperbola applying vertical translation of the graph
Sketch a hyperbola applying reflection of the graph across the x or y axis
Sketching basic hyperbolas in the from y=a/x where a is a positive integer
Find the radius and centre of a circle given the equation or graph
Finding points of intersection of a line with a circle
Find the radius and centre of a circle by completing the square
Sketching semi-circles
Sketching a circle
Sketch an exponential function applying reflection of the graph across the x or y axis
Sketch an exponential function applying vertical translation of the graph
Sketch an exponential function applying horizontal translation of the graph
Sketch an exponential function with dilation
Sketching exponentials
Sketch a basic logarithmic function
Sketch a logarithmic function with transformations
Sketch piecewise defined functions
Sketching the absolute value of a non-linear function on the number plane
Sketching the absolute value of a linear function on the number plane
Sketch a function applying multiple transformations
Sketch a region defined by a non-linear inequality
Intersection of regions
Sketch a region defined by a linear inequality
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