Topic outline

  • PLO: B1

    Demonstrate an understanding of operations on, and compositions of, functions.

    Write a function h(x) as the sum, difference, product or quotient of two or more functions.

    Determine the value of the composition of functions when evaluated at a point (from an equation and a graph, including: f (f(a)), f(g(a)) and g(f(a)) .

    Determine, given the equations of two functions f(x) and g(x), the equation of the composite
    function: f ( f (x)), f (g ( x)) and g ( f ( x)) and explain any restrictions.

    Write a function h(x) as the composition of two or more functions.

    Write a function h(x) by combining two or more functions through operations on, and
    compositions of, functions.

    ASSESSMENT: PLO: B1 Friday Sept.15/17

    RE-ASSESSMENT: 

  • PLO: B2

    Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations.

    Compare the graphs of a set of functions of the form y – k = f (x) to the graph of y = f (x), and generalize, using inductive reasoning, a rule about the effect of k.

    Compare the graphs of a set of functions of the form y = f (x − h) to the graph of y = f (x), and generalize, using inductive reasoning, a rule about the effect of h.

    Compare the graphs of a set of functions of the form y − k = f (x − h) to the graph of y = f (x), and generalize, using inductive reasoning, a rule about the effects of h and k.

    Sketch the graph of y − k = f (x) , y = f (x − h) or y − k = f (x − h) for given values of h and k, given a sketch of the function y = f (x) , where the equation of y = f (x) is not given.

    Write the equation of a function whose graph is a vertical and/or horizontal translation of the graph of the function y = f (x) .

    Practice Questions

    ASSESSMENT: 

  • PLO: B3

    Demonstrate an understanding of the effects of horizontal and vertical stretches on the graphs of functions and their related equations.

    Compare the graphs of a set of functions of the form y = af (x) to the graph of y = f (x) , and
    generalize, using inductive reasoning, a rule about the effect of a.


    Compare the graphs of a set of functions of the form y = f (bx) to the graph of y = f (x) , and
    generalize, using inductive reasoning, a rule about the effect of b.


    Compare the graphs of a set of functions of the form y =af (bx) to the graph of y = f (x) ,
    and generalize, using inductive reasoning, a rule about the effects of a and b.


    Sketch the graph of y = af (x) , y = f (bx) or y =af (bx) for given values of a and b, given a
    sketch of the function y = f(x), where the equation of y = f (x) is not given.


    Write the equation of a function, given its graph which is a vertical and/or horizontal stretch
    of the graph of the function y = f (x) .

    Practice Work

    Assessment


  • PLO: B4

    Apply translations and stretches to the graphs and equations of functions.

    Sketch the graph of the function y − k = af (b(x − h)) for given values of a, b, h and k, given
    the graph of the function y = f (x) , where the equation of y = f (x) is not given.


    Write the equation of a function, given its graph which is a translation and/or stretch of the
    graph of the function y = f (x) .

    Practice Questions

    Assessment


  • PLO: B5

    Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections through the:  x-axis, y-axis, line y = x.

    Generalize the relationship between the coordinates of an ordered pair and the coordinates of
    the corresponding ordered pair that results from a reflection through the x-axis, the y-axis or
    the line y = x.

    Sketch the reflection of the graph of a function y = f (x) through the x-axis, the y-axis or the
    line y = x, given the graph of the function y = f (x) , where the equation of y = f (x) is not
    given.

    Generalize, using inductive reasoning, and explain rules for the reflection of the graph of the
    function y = f (x) through the x-axis, the y-axis or the line y = x.

    Sketch the graphs of the functions y = −f (x), y = f (−x) and x = −f (y), given the graph of the
    function y = f (x), where the equation of y = f (x) is not given.

    Write the equation of a function, given its graph which is a reflection of the graph of the
    function y = f (x) through the x-axis, the y-axis or the line y = x.

    Practice Questions

     

  • PLO: B6

    Demonstrate an understanding of inverses of relations.

    Explain how the transformation (x, y) => (y, x) can be used to sketch the inverse of a relation.

    Sketch the graph of the inverse relation, given the graph of a relation.

    Determine if a relation and its inverse are functions.

    Determine restrictions on the domain of a function in order for its inverse to be a function.

    Determine the equation and sketch the graph of the inverse relation, given the equation of a linear or quadratic relation.

    Explain the relationship between the domains and ranges of a relation and its inverse.

    Determine, algebraically or graphically, if two functions are inverses of each other.

    Assessments:


  • PLO: B13

    Graph and analyze radical functions (limited to functions involving one radical).

    Assessment:


  • PLO: B11

    Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

    Assessment:


  • PLO: B12

    Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 )

    Assessment:


  • PLO: B7 & B8

    Demonstrate an understanding of logarithms including the product, quotient and power laws of logarithms.

    Practice:

    Assessment:


  • PLO: A1

    Demonstrate an understanding of angles in standard position, expressed in degrees and radians.

    Practice:

    Assessment:


  • PLO: A3

    Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees.

    Practice:


    Assessment:


  • PLO: A5

    Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians.