Functions

Worked examples (10)extended set

• 1Domain and range of a linear function
• 2Domain restricted by a square root
• 3Domain restricted by a denominator
• 4Range of a quadratic function
• 5Range over a restricted domain
• 6Combining two restrictions
• 7Range and inverse from a mapping diagram
• 8Range of a reciprocal function from its graph
• 9Choosing a domain to fit a given range
• 10Range from a discrete domain

Worked examples (9)extended set

• 1Logarithms from the definition
• 2Combining logarithms
• 3The power law
• 4Solving an exponential equation
• 5Solving a logarithmic equation
• 6Exponential growth with logarithms
• 7The graph of a logarithm as a reflection
• 8Exponential model from a graph, solved with logarithms
• 9When one population overtakes another

Worked examples (13)extended set

• 1Evaluating composite functions
• 2Composite function as an expression
• 3Finding an inverse function
• 4Inverse where the variable appears twice
• 5Solving an equation involving an inverse
• 6Composing a function with itself
• 7Reversing a function machine
• 8Composite and inverse values read from graphs
• 9Inverse of a quadratic and its reflection in y = x
• 10Substituting an expression, and the inverse
• 11Inverse of an exponential function
• 12Composite function as a quadratic
• 13Composite of two linear functions

Worked examples (9)extended set

• 1Key features of a quadratic graph
• 2Completing the square to find the vertex
• 3Completing the square with a coefficient
• 4A negative quadratic
• 5Condition for equal roots
• 6Optimisation in context
• 7Completed-square form from a drawn graph
• 8Height of a ball from a quadratic graph
• 9Will the lorry fit under the arch?

Worked examples (12)extended set

• 1Sketching a cubic from its roots
• 2The reciprocal graph
• 3Solving by intersection of two graphs
• 4Exponential graphs
• 5Reading solutions from a drawn graph
• 6Rearranging to reuse a drawn graph
• 7Matching equations to sketch graphs
• 8Solving equations with a curve and a straight line
• 9Counting solutions with a cubic graph
• 10Asymptotes and a drawn line on a reciprocal graph
• 11Sketching a cubic with a repeated root
• 12Drawing a cubic and solving a related equation