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Master Grade 11 Functions (MCR3U)

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Find the right Ontario Grade 11 course

Grade 11 Functions, University Preparation (MCR3U)

Grade 11 Functions and Applications, University/College Preparation (MCF3M)

Grade 11 Foundations for College Mathematics, College Preparation (MBF3C)

Grade 11 Mathematics for Work and Everyday Life, Workplace Preparation (MEL3E)

Ontario Grade 11 Functions (MCR3U) Help OnlineHelp

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ON.OE.11F.A1.1

11F.A1.1: Explain the meaning of the term function, and distinguish a function from a relation that is not a function, through investigation of linear and quadratic relations using a variety of representations (i.e., tables of values, mapping diagrams, graphs, function machines, equations) and strategies (e.g., identifying a one-to-one or many-to-one mapping; using the vertical-line test)

ON.OE.11F.A1.2

11F.A1.2: Represent linear and quadratic functions using function notation, given their equations, tables of values, or graphs, and substitute into and evaluate functions

ON.OE.11F.A1.3

11F.A1.3: Explain the meanings of the terms domain and range, through investigation using numeric, graphical, and algebraic representations of the functions f(x) = x, f(x) = x^2, f(x) = ?x, and f(x) = 1/x; describe the domain and range of a function appropriately; and explain any restrictions on the domain and range in contexts arising from real-world applications

ON.OE.11F.A1.4

11F.A1.4: Relate the process of determining the inverse of a function to their understanding of reverse processes

ON.OE.11F.A1.5

11F.A1.5: Determine the numeric or graphical representation of the inverse of a linear or quadratic function, given the numeric, graphical, or algebraic representation of the function, and make connections between the graph of a function and the graph of its inverse

ON.OE.11F.A1.6

11F.A1.6: Determine the relationship between the domain and range of a function and the domain and range of the inverse relation, and determine whether or not the inverse relation is a function

ON.OE.11F.A1.8

11F.A1.8: Determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y = af(k(x ? d)) + c, and describe these roles in terms of transformations on the graphs of f(x) = x, f(x) = x^2, f(x) = ?x, and f(x) = 1/x

ON.OE.11F.A1.9

11F.A1.9: Sketch graphs of y = af(k(x ? d)) + c by applying one or more transformations to the graphs of f(x) = x, f(x) = x^2, f(x) = ?x, and f(x) = 1/x, and state the domain and range of the transformed functions

ON.OE.11F.A2.1

11F.A2.1: Determine the number of zeros of a quadratic function, using a variety of strategies

ON.OE.11F.A2.2

11F.A2.2: Determine the maximum or minimum value of a quadratic function whose equation is given in the form f(x) = ax^2 + bx + c, using an algebraic method

ON.OE.11F.A2.3

11F.A2.3: Solve problems involving quadratic functions arising from real-world applications and represented using function notation

ON.OE.11F.A2.4

11F.A2.4: Determine, through investigation, the transformational relationship among the family of quadratic functions that have the same zeros, and determine the algebraic representation of a quadratic function, given the real roots of the corresponding quadratic equation and a point on the function

ON.OE.11F.A2.5

11F.A2.5: Solve problems involving the intersection of a linear function and a quadratic function graphically and algebraically

ON.OE.11F.A3.1

11F.A3.1: Simplify polynomial expressions by adding, subtracting, and multiplying

ON.OE.11F.A3.2

11F.A3.2: Verify, through investigation with and without technology, that ?ab = ?a ? ?b, a ? 0, b ? 0, and use this relationship to simplify radicals and radical expressions obtained by adding, subtracting, and multiplying

ON.OE.11F.A3.3

11F.A3.3: Simplify rational expressions by adding, subtracting, multiplying, and dividing, and state the restrictions on the variable values

ON.OE.11F.B1.1

11F.B1.1: Graph, with and without technology, an exponential relation, given its equation in the form y = a^x (a > 0, a ? 1), define this relation as the function f(x) = a^x, and explain why it is a function

ON.OE.11F.B1.2

11F.B1.2: Determine, through investigation using a variety of tools and strategies, the value of a power with a rational exponent

ON.OE.11F.B1.3

11F.B1.3: Simplify algebraic expressions containing integer and rational exponents, and evaluate numeric expressions containing integer and rational exponents and rational bases

ON.OE.11F.B2.2

11F.B2.2: Determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y = af(k(x ? d)) + c, and describe these roles in terms of transformations on the graph of f(x) = a^x (a > 0, a ? 1)

ON.OE.11F.B2.4

11F.B2.4: Determine, through investigation using technology, that the equation of a given exponential function can be expressed using different bases, and explain the connections between the equivalent forms in a variety of ways

ON.OE.11F.B2.5

11F.B2.5: Represent an exponential function with an equation, given its graph or its properties

ON.OE.11F.B3.2

11F.B3.2: Identify exponential functions, including those that arise from real-world applications involving growth and decay, given various representations, and explain any restrictions that the context places on the domain and range

ON.OE.11F.C1.1

11F.C1.1: Make connections between sequences and discrete functions, represent sequences using function notation, and distinguish between a discrete function and a continuous function

ON.OE.11F.C1.5

11F.C1.5: Determine, through investigation, recursive patterns in the Fibonacci sequence, in related sequences, and in Pascal's triangle, and represent the patterns in a variety of ways

ON.OE.11F.C1.6

11F.C1.6: Determine, through investigation, and describe the relationship between Pascal's triangle and the expansion of binomials, and apply the relationship to expand binomials raised to whole-number exponents

ON.OE.11F.C2.1

11F.C2.1: Identify sequences as arithmetic, geometric, or neither, given a numeric or algebraic representation

ON.OE.11F.C2.3

11F.C2.3: Determine the formula for the sum of an arithmetic or geometric series, through investigation using a variety of tools and strategies, and apply the formula to calculate the sum of a given number of consecutive terms

ON.OE.11F.C3.1

11F.C3.1: Make and describe connections between simple interest, arithmetic sequences, and linear growth, through investigation with technology

ON.OE.11F.C3.2

11F.C3.2: Make and describe connections between compound interest, geometric sequences, and exponential growth, through investigation with technology

ON.OE.11F.C3.5

11F.C3.5: Explain the meaning of the term annuity, and determine the relationships between ordinary simple annuities, geometric series, and exponential growth, through investigation with technology

ON.OE.11F.D1.1

11F.D1.1: Determine the exact values of the sine, cosine, and tangent of the special angles: 0?, 30?, 45?, 60?, and 90?

ON.OE.11F.D1.3

11F.D1.3: Determine the measures of two angles from 0? to 360? for which the value of a given trigonometric ratio is the same

ON.OE.11F.D1.4

11F.D1.4: Define the secant, cosecant, and cotangent ratios for angles in a right triangle in terms of the sides of the triangle, and relate these ratios to the cosine, sine, and tangent ratios

ON.OE.11F.D1.5

11F.D1.5: Prove simple trigonometric identities, using the Pythagorean identity sin^2 x + cos^2 x = 1; the reciprocal identities secx = 1/cosx, cscx = 1/sinx, and cotx = 1/tanx; the quotient identity tanx = sinx/cosx; and the Pythagorean identities 1 + tan^2 x = sec^2 x and 1 + cot^2 x = csc^2 x

ON.OE.11F.D1.6

11F.D1.6: Pose problems involving right triangles and oblique triangles in two-dimensional settings, and solve these and other such problems using the primary trigonometric ratios, the cosine law, and the sine law (including the ambiguous case)

ON.OE.11F.D2.1

11F.D2.1: Describe key properties of periodic functions arising from real-world applications, given a numeric or graphical representation

ON.OE.11F.D2.5

11F.D2.5: Determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y = af(k(x ? d)) + c, where f(x) = sinx or f(x) = cosx with angles expressed in degrees, and describe these roles in terms of transformations on the graphs of f(x) = sinx and f(x) = cosx

ON.OE.11F.D2.8

11F.D2.8: Represent a sinusoidal function with an equation, given its graph or its properties

ON.OE.11F.D3.2

11F.D3.2: Identify periodic and sinusoidal functions, including those that arise from real-world applications involving periodic phenomena, given various representations, and explain any restrictions that the context places on the domain and range
Complete Ontario Grade 11 Functions, University Preparation (MCR3U) Coverage

Grade 11 Functions (MCR3U) Lessons

69

Video Explanations

406

Practice Problems

758

Ontario Standards

100% Aligned

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Frequently Asked Questions

Everything you need to know about mastering Grade 11 Functions (MCR3U)

What does Grade 11 Functions (MCR3U) coverage include?

Complete MCR3U curriculum with video lessons on functions, exponential relations, trigonometry, sequences, and financial applications. Includes practice problems, step-by-step solutions, and progress tracking for every topic.

How does the AI photo search work?

Take a photo of any functions problem, and our AI finds the exact lesson teaching that concept. It's like having a personal tutor who knows exactly what you need for MCR3U success.

Are the teachers certified Ontario educators?

Yes! Our teachers are Canadian certified Ontario educators who understand MCR3U curriculum and create lessons specifically for Ontario university preparation standards.

Can I use StudyPug on my phone or tablet?

Absolutely! StudyPug works on desktop, tablet, and mobile. Your progress syncs automatically so you can study for Grade 11 Functions anywhere, anytime.

How will StudyPug help me prepare for university mathematics?

We teach the exact MCR3U concepts needed for university readiness and include practice questions that build the problem-solving skills Ontario universities expect. Students report significantly improved confidence and grades.

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