Working with Functions

Scheme of work: GCSE Higher: Year 11: Term 2: Working with Algebraic Fractions

Plot graphs of equations that correspond to straight-line graphs in the coordinate plane
Recognise, sketch and interpret graphs of linear and non-linear functions
Identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement.

Where appropriate, interpret simple expressions as functions with inputs and outputs; interpret the reverse process as the inverse function; interpret the succession of two functions as a composite function.
Sketch translations and reflections of a given function
Calculate or estimate gradients of graphs (including quadratic and other non-linear graphs),
Find approximate solutions to equations numerically using iteration

A function is any algebraic expression in which x is the only variable. It is denoted as f(x)
Understanding the notation for transformation of functions is critical to accessing this topic.
- f(x) ± a = Vertical Translation
- f(x ± a) = Horizontal Translation
- af(x) = Horizontal stretch
- f(ax) = Vertical stretch
Composite functions combine more than one function to an input.
Inverse functions perform the opposite operation to a function.
A gradient function calculates and approximate the instantaneous rate of change for given values of x.
Iterative solutions can diverge or converge.

-f(x) is often incorrectly taken as a reflection in the y-axis rather than the x.
f(x + a) translates a unit to the left rather than to the right.
Students often struggle with writing the equation of the new function after a transformation.
Students need to be precise when drawing the transformed function.
The order of a composite function is often confused, fg(x) -> g acts on x first, then f acts on the result.
Students can often differentiate functions with little understanding of how to apply the gradient function correctly.