Master: Relations, Functions & Graphs

Master: Relations, Functions & Graphs

Course Modules

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1. Explain concepts associated with relations; concept of a relation, types of relation, examples and non-examples of relations, domain, range, image, co-domain.
 
Move done incomplete Curriculum Requirements for Specific Objective 1 Curriculum Requirements for Specific Objective 1
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Move done incomplete Domain and range (CK-12) Domain and range (CK-12)
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Move done incomplete Functions and relations - book extract (Commonwealth of Learning) Functions and relations - book extract (Commonwealth of Learning)
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Move done incomplete Relations and functions (Open High School) Relations and functions (Open High School)
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2. Represent a relation in various ways; set of ordered pairs, arrow diagrams, graphically, algebraically.
 
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Move done incomplete Represent relation and function in different ways (CK-12) Represent relation and function in different ways (CK-12)
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Move done incomplete Relations and ordered pairs (CK-12) Relations and ordered pairs (CK-12)
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Move done incomplete Represent a relation using a graph (CK-12) Represent a relation using a graph (CK-12)
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Move done incomplete Relations and functions (Open High School) Relations and functions (Open High School)
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3. State the characteristics that define a function; concept of a function, examples and non-examples of functions.
 
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Move done incomplete Definition of a function (Everything Maths) Definition of a function (Everything Maths)
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Move done incomplete Relations, graphs and functions (OpenAlgebra.com) Relations, graphs and functions (OpenAlgebra.com)
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Move done incomplete Functions (mathcentre.ac.uk) Functions (mathcentre.ac.uk)
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4. Use functional notation; for example f : x x2; or f(x) = x2 as well as y = f(x) for given domains.
 
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Move done incomplete Functions and function notation (OpenAlgebra.com) Functions and function notation (OpenAlgebra.com)
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Move done incomplete Function notation (mathcentre.ac.uk) Function notation (mathcentre.ac.uk)
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Move done incomplete Relations and functions (Open High School) Relations and functions (Open High School)
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5. Distinguish between a relation and a function; ordered pairs, arrow diagram, graphically (vertical line test).
 
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Move done incomplete Determine whether a relation is a function - vertical line test (CK-12) Determine whether a relation is a function - vertical line test (CK-12)
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Move done incomplete Introduction to functions, relations and vertical line test (Open High School) Introduction to functions, relations and vertical line test (Open High School)
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6. Draw and interpret graphs of linear functions; concept of linear function, types of linear function (y = c; x = k; y = mx + c; where m, c and k are real numbers).
 
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Move done incomplete Linear graph (Nayland School) Linear graph (Nayland School)
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Move done incomplete Linear functions (mathcentre.ac.uk) Linear functions (mathcentre.ac.uk)
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Move done incomplete Equations of Horizontal and Vertical Lines (y=c and x=k) (Open High School) Equations of Horizontal and Vertical Lines (y=c and x=k) (Open High School)
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7. Determine the intercepts of the graph of linear functions; x-intercepts and y-intercepts, graphically and algebraically.
 
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Move done incomplete Straight line graph - intercept method (Nayland School) Straight line graph - intercept method (Nayland School)
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Move done incomplete Graph using intercepts (OpenAlgebra.com) Graph using intercepts (OpenAlgebra.com)
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Move done incomplete Graph linear equations (Open High School) Graph linear equations (Open High School)
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8. Determine the gradient of a straight line; concept of slope.
 
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Move done incomplete Gradient of straight line (Nayland School) Gradient of straight line (Nayland School)
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Move done incomplete Introduction to Slope in y =mx+c (Open High School) Introduction to Slope in y =mx+c (Open High School)
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Move done incomplete Gradient straight line (mathcentre.ac.uk) Gradient straight line (mathcentre.ac.uk)
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9. Determine the equation of a straight line; the graph of the line. The co-ordinates of two points on the line. The gradient and one point on the line. One point on the line and its relationship to another line.
 
Move done incomplete Curriculum Requirements for Specific Objective 9 Curriculum Requirements for Specific Objective 9
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Move done incomplete Equation of straight line (mathcentre.ac.uk) Equation of straight line (mathcentre.ac.uk)
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Move done incomplete Graph using y intercept and slope (OpenAlgebra.com) Graph using y intercept and slope (OpenAlgebra.com)
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Move done incomplete Find equation of line given any point on the line and slope (OpenAlgebra.com) Find equation of line given any point on the line and slope (OpenAlgebra.com)
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Move done incomplete Slope-Intercept Form (Open High School) Slope-Intercept Form (Open High School)
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Move done incomplete Gradients Part 2 (Mastering Mathematics on YouTube) Gradients Part 2 (Mastering Mathematics on YouTube)
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Move done incomplete Gradients Part 3 (Mastering Mathematics on YouTube) Gradients Part 3 (Mastering Mathematics on YouTube)
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10. Solve problems involving the gradient of parallel and perpendicular lines.
 
Move done incomplete Curriculum Requirements for Specific Objective 10 Curriculum Requirements for Specific Objective 10
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Move done incomplete Gradient straight line (mathcentre.ac.uk) Gradient straight line (mathcentre.ac.uk)
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Move done incomplete Parallel and perpendicular lines (OpenAlgebra.com) Parallel and perpendicular lines (OpenAlgebra.com)
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Move done incomplete Writing linear equations (Open High School) Writing linear equations (Open High School)
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Move done incomplete Gradients Part 1 (Mastering Mathematics on Youtube) Gradients Part 1 (Mastering Mathematics on Youtube)
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11. Determine from co-ordinates on a line segment: (a) the length; (b) the co-ordinates of the midpoint; the concept of magnitude or length, concept of midpoint.
 
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Move done incomplete Midpoint formula (CK-12) Midpoint formula (CK-12)
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Move done incomplete Mid-point of line segment (Everything Maths) Mid-point of line segment (Everything Maths)
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Move done incomplete Distance between two points (Everything Maths) Distance between two points (Everything Maths)
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Move done incomplete Distance and mid-point formulas (OpenAlgebra.com) Distance and mid-point formulas (OpenAlgebra.com)
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Move done incomplete Distance between 2 points and midpoint of line segment (mathcentre.ac.uk) Distance between 2 points and midpoint of line segment (mathcentre.ac.uk)
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12. Solve graphically a system of two linear equations in two variables.
 
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Move done incomplete Solve system of linear equations graphically (Open High School) Solve system of linear equations graphically (Open High School)
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Move done incomplete Solve linear systems by graphing (OpenAlgebra.com) Solve linear systems by graphing (OpenAlgebra.com)
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13. Represent the solution of linear inequalities in one variable using: (a) set notation; (b) the number line; (c) graph.
 
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Move done incomplete Linear inequalities - book extract (CK-12) Linear inequalities - book extract (CK-12)
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Move done incomplete Linear inequalities - solve and express on number line (Open High School) Linear inequalities - solve and express on number line (Open High School)
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14. Draw a graph to represent a linear inequality in two variables.
 
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Move done incomplete Graph linear inequalities with 2 variables (OpenAlgebra.com) Graph linear inequalities with 2 variables (OpenAlgebra.com)
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Move done incomplete Graphing linear inequality in 2 variables (Open High School) Graphing linear inequality in 2 variables (Open High School)
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15. Use linear programming techniques to solve problems involving two variables.
 
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Move done incomplete Linear programming (Everything Maths) Linear programming (Everything Maths)
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Move done incomplete Linear programming and the feasible region (Everything Maths) Linear programming and the feasible region (Everything Maths)
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Move done incomplete Linear programming - terminology explained (Everything Maths) Linear programming - terminology explained (Everything Maths)
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Move done incomplete Application of Systems of Inequalities: Linear Programming - book extract (Boundless) Application of Systems of Inequalities: Linear Programming - book extract (Boundless)
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Move done incomplete Linear programming - Mathematics Gr 11 - book extract (FHSST) Linear programming - Mathematics Gr 11 - book extract (FHSST)
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16. Derive composite functions; composite function, for example, fg, f2 given f and g. Non-commutativity of composite functions (fg≠gf).
 
Move done incomplete Curriculum Requirements for Specific Objective 16 Curriculum Requirements for Specific Objective 16
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Move done incomplete Function composition (OpenAlgebra.com) Function composition (OpenAlgebra.com)
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Move done incomplete Functions and relations - book extract (Commonwealth of Learning) Functions and relations - book extract (Commonwealth of Learning)
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Move done incomplete Composite functions (Open High School) Composite functions (Open High School)
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17. State the relationship between a function and its inverse; the concept of the inverse of a function.
 
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Move done incomplete A function and its inverse (Everyday Maths) A function and its inverse (Everyday Maths)
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Move done incomplete Inverse functions (Mathcentre) Inverse functions (Mathcentre)
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Move done incomplete Inverse functions and relations (OpenAlgebra.com) Inverse functions and relations (OpenAlgebra.com)
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Move done incomplete Functions and Relations (Commonwealth of Learning) Functions and Relations (Commonwealth of Learning)
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Move done incomplete Inverse functions and relations (Open High School) Inverse functions and relations (Open High School)
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18. Derive the inverse of a function; f-1, (fg)-1.
 
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Move done incomplete Inverse functions and relations (OpenAlgebra.com) Inverse functions and relations (OpenAlgebra.com)
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Move done incomplete Inverse functions - book extract (Saylor.org) Inverse functions - book extract (Saylor.org)
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Move done incomplete Functions and relations - book extract (Commonwealth of Learning) Functions and relations - book extract (Commonwealth of Learning)
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Move done incomplete Inverse functions (mathcentre.ac.uk) Inverse functions (mathcentre.ac.uk)
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19. Evaluate f(a), f-1(a), fg(a), (fg)-1(a); Where a∈ℜ.
 
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Move done incomplete Inverse functions - book extract (Saylor.org) Inverse functions - book extract (Saylor.org)
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Move done incomplete Mathematics12 functions and relations (Commonwealth of Learning) Mathematics12 functions and relations (Commonwealth of Learning)
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20. Use the relationship (fg)-1= g-1 f-1; the concept of the inverse of a function, determining the inverse of a given function.
 
Move done incomplete Curriculum Requirements for Specific Objective 20 Curriculum Requirements for Specific Objective 20
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Move done incomplete Inverse functions (Saylor.org) Inverse functions (Saylor.org)
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Move done incomplete Functions and relations (Commonwealth of Learning) Functions and relations (Commonwealth of Learning)
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21. Draw and interpret graphs of a quadratic function to determine: (a) the elements of the domain that have a given image; (b) the image of a given element in the domain; (c) the maximum or minimum value of the function; (d) the equation of the axis of symmetry; (e) the interval of the domain for which the elements of the range may be greater than or less than a given point; (f) an estimate of the value of the gradient at a given point; (g) intercepts of the function Concepts of gradient of a curve at a point, tangent, turning point. Roots of the equation.
 
Move done incomplete Curriculum Requirements for Specific Objective 21 Curriculum Requirements for Specific Objective 21
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Move done incomplete Quadratic function (Everything Maths) Quadratic function (Everything Maths)
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Move done incomplete Graphing parabolas (OpenAlgebra.com) Graphing parabolas (OpenAlgebra.com)
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Move done incomplete Graphing Quadratic Functions (Open High School) Graphing Quadratic Functions (Open High School)
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22. Determine the axis of symmetry, maximum or minimum value of a quadratic function expressed in the form a(x + h)2 + k.
 
Move done incomplete Curriculum Requirements for Specific Objective 22 Curriculum Requirements for Specific Objective 22
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Move done incomplete Quadratic function (Everything Maths) Quadratic function (Everything Maths)
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Move done incomplete More Graphs of Quadratic Functions (Open High School) More Graphs of Quadratic Functions (Open High School)
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Move done incomplete More graphing examples Quadratic Functions (Open High School) More graphing examples Quadratic Functions (Open High School)
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Move done incomplete From general form to vertex form (Open High School) From general form to vertex form (Open High School)
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23. Sketch graph of quadratic function expressed in the form a(x+h)2 + k and determine number of roots.
 
Move done incomplete Curriculum Requirements for Specific Objective 23 Curriculum Requirements for Specific Objective 23
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Move done incomplete Quadratic Function (Everything Maths) Quadratic Function (Everything Maths)
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Move done incomplete Quadratic Functions of the Form: f(x) = a(x-h)^2 + k (Boundless.com) Quadratic Functions of the Form: f(x) = a(x-h)^2 + k (Boundless.com)
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24. Draw and interpret the graphs of other non-linear functions. Optional Specific Objective. y=axn where n = -1,-2 and +3.
 
Move done incomplete Curriculum Requirements for Specific Objective 24 Curriculum Requirements for Specific Objective 24
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Move done incomplete Hyperbola, cubic and exponential graphs (algebra2c.wikispaces) Hyperbola, cubic and exponential graphs (algebra2c.wikispaces)
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Move done incomplete Quadratics and Other Non-linear Graphs - book extract (Commonwealth of Learning) Quadratics and Other Non-linear Graphs - book extract (Commonwealth of Learning)
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Move done incomplete Hyperbola y = a/x (Nayland School) Hyperbola y = a/x (Nayland School)
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Move done incomplete Graph of y = ax^3 (AmericanoMath) Graph of y = ax^3 (AmericanoMath)
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Move done incomplete Cubic function (Nayland School) Cubic function (Nayland School)
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25. Draw and interpret distance-time graphs and speed-time graphs (straight line only) to determine: (a) distance; (b) time; (c) speed; (d) magnitude of acceleration.
 
Move done incomplete Curriculum Requirements for Specific Objective 25 Curriculum Requirements for Specific Objective 25
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Move done incomplete Exploring distance time graphs - an example (OpenLearn) Exploring distance time graphs - an example (OpenLearn)
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Move done incomplete Motion graphs (Everything Science) Motion graphs (Everything Science)
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Move done incomplete Time, Velocity and Speed (CNX) Time, Velocity and Speed (CNX)
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Move done incomplete Distance-Time Graphs - book extract (Commonwealth of Learning) Distance-Time Graphs - book extract (Commonwealth of Learning)
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Self Assessment Activities
 
Move done incomplete Relations, Functions & Graphs Self Assessment Quiz Relations, Functions & Graphs Self Assessment Quiz
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