Functions and Applications, Grade 11 (University/College)

Unit 1: Quadratic Functions

Expanding, factoring, and solving quadratic expressions and equations; understanding functions and their domain and range; graphing quadratic functions in standard, vertex, and factored form; and modelling and solving real-world problems with quadratic functions.

• Posing and solving real-world quadratic problems
• Representing situations with quadratic expressions and expanding them
• Factoring quadratic expressions
• Solving quadratic equations by factoring
• Connecting factors to the graph's x-intercepts
• Exploring and applying the quadratic formula
• The discriminant and the number of real roots
• Comparing strategies for finding real roots

• What makes a relation a function
• Substituting into and evaluating function notation
• What domain and range mean
• Domain and range restrictions in real-world contexts

• What a, h, and k do to a parabola's graph
• Sketching quadratic graphs using transformations
• Converting vertex form to standard form
• Converting standard form to vertex form by completing the square
• Sketching a quadratic graph from factored form
• Comparing what standard, vertex, and factored form each reveal
• Sketching a quadratic graph from standard form and identifying its key features

• Collecting and graphing data that fits a quadratic model
• Finding the quadratic equation that best fits a data set
• Solving real-world problems from a quadratic function's equation

Unit 2: Exponential Functions

Rational exponents and exponent rules; graphing and identifying exponential functions and their properties; modelling growth and decay; and compound interest and annuities.

• What a power with a rational exponent means
• Evaluating expressions with integer and rational exponents
• Exponent rules for multiplying, dividing, and powers of powers

• Graphing an exponential relation and defining it as a function
• Key properties of exponential functions
• Telling exponential, linear, and quadratic functions apart

• Collecting and graphing data that fits an exponential model
• Identifying exponential growth and decay in real-world contexts
• Solving real-world problems with exponential graphs and equations

• Comparing simple and compound interest
• Using the compound interest formula to find amount or principal
• Compound interest is exponential growth
• Using the TVM Solver to find interest rate or number of periods
• What an annuity is
• How changing an annuity's conditions affects it
• Solving for an annuity's amount, present value, or payment

Unit 3: Trigonometric Functions

Solving triangle problems with the primary ratios, the sine law, and the cosine law; understanding periodic relationships; graphing and transforming the sine function; and modelling and solving real-world problems with sine functions.

• Solving right-triangle problems with primary trig ratios
• Solving problems with two right triangles
• Verifying the sine law and the cosine law
• Choosing between the sine law and the cosine law
• Solving real-world problems with the sine or cosine law

• Key properties of periodic functions
• Predicting future behaviour of a periodic relationship
• Connecting the sine ratio to the sine function
• Sketching f(x) = sin x and its key properties
• Connecting real-world changes to graph transformations
• What a, c, and d do to the sine function's graph
• Sketching sine function transformations and stating domain/range

• Collecting and graphing data that fits a sine model
• Identifying periodic and sinusoidal functions in real-world contexts
• Posing and solving problems with sine functions