MATHS METHODS (UNITS 3 & 4)

Functions & graphs

This is a ‘pre-calculus’ topic that covers the foundations of functions & graphs. It can be helpful for students, who are about to begin studying calculus.

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TOPIC OVERVIEW

Topic 1: Functions & graphs

The ‘Functions & Graphs’ topic refers to the following:

This includes the following key areas:

  • Use functional notation to evaluate a function
  • Determine the domain and range of a function
  • Draw the graph of a function
  • Find the zeros of a function
  • Recognise a function from a table of values
  • Make new functions from two or more given functions
  • Describe the symmetry properties of a function.

This includes the following key areas:

  • Calculate the slope of a linear function and interpret its meaning
  • Recognise the degree of a polynomial
  • Find the roots of a quadratic polynomial
  • Describe the graphs of basic odd and even polynomial functions
  • Identify a rational function
  • Describe the graphs of power and root functions
  • Explain the difference between algebraic and transcendental functions
  • Graph a piecewise-defined function
  • Sketch the graph of a function that has been shifted, stretched, or reflected from its initial
    graph position.

This includes the following key areas:

  • Convert angle measures between degrees and radians
  • Recognise the triangular and circular definitions of the basic trigonometric functions
  • Write the basic trigonometric identities
  • Identify the graphs and periods of the trigonometric functions
  • Describe the shift of a sine or cosine graph from the equation of the function.

This includes the following key areas:

  • Determine the conditions for when a function has an inverse
  • Use the horizontal line test to recognise when a function is one-to-one
  • Find the inverse of a given function
  • Draw the graph of an inverse function
  • Evaluate inverse trigonometric functions.

This includes the following key areas:

  • Identify the form of an exponential function
  • Explain the difference between the graphs of x^b and b^x
  • Recognise the significance of the number e
  • Identify the form of a logarithmic function
  • Explain the relationship between exponential and logarithmic functions
  • Describe how to calculate a logarithm to a different base
  • Identify the hyperbolic functions, their graphs, and basic identities.

Types of help available

We can assist you, via the following range of ‘help options’.

Question bank

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Student Help-desk

If you have a quick question, use your ‘Access pass’ to ask for teacher help via the ‘Student Help-desk’.

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If you’d like help with a specific section / topic, or are stuck on a few questions, use your ‘Access pass’ to book a 30-minute ‘Solo Tutorial’, via an interactive whiteboard.

Resource Hub

You can buy an ‘Access pass’ to access the ‘Student help-desk’, ‘Solo tutorials’, or ‘Self-paced workshops’.

Self-paced workshops

Join an workshop to master a key area of this topic. Includes modern & innovative resources, as well as a ’10-min Access pass’ to ask for help via the ‘Student help-desk’.

Live-stream tutorials

Throughout the year, we’ll be streaming online maths sessions, which students can join by buying a ticket at the ‘Resource hub’. More details soon.