VIDEOS & Course Resources and Study Material

Relations and Functions

Specific Outcome 1

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

• given their equations, sketch the graph of a function that is the sum, difference, product, quotient, or composition of two functions
• given their graphs, sketch the graph of a function that is the sum, difference, product, , or composition of two functions
• EXCELLENCE - given their graphs, sketch the graph of a function that is the quotient of two functions
• determine the domain and range of a function that is the sum, difference, product, or quotient of two functions, with technology
• write a function, h(x), as:
  • –the sum or difference of functions
  • –the product or quotient of two functions
  • EXCELLENCE - 3 Functions
  • –a single composition
  • E.g., h(x)=f(f(x)) or h(x) = f(g(x)
  • –identify any restriction on h(x) which results from the operation of two functions
• determine the value of the composition of two or three functions at a point
• E.g f(f(a)), f(g(a)) or g(f(h(a)))
• EXCELLENCE -
• 2 or more compositions =
• f(x)g(x) + h(x)
• or h(x) = g(x) + f(g(x))

Specific Outcome 2

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

• perform, analyze, and describe graphically or algebraically:
  • a combination of transformations involving stretches and/or translations VIDEO
  • VIDEO2-Better
  • a combination of transformations involving reflections and/or translations
  • a combination of transformations involving reflections and/or stretches
  • a horizontal stretch and/or reflection in the y-axis and a translation where the parameter b is removed through factoring
  • VIDEO

• EXCELLENCE - b is NOT removed.
• EXCELLENCE - stretch, reflection AND translation.
• given the function in equation or graphical form or mapping notation. VIDEO

Specific Outcome 3

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

Specific Outcome 4

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

Specific Outcome 5

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

Specific Outcome 6

Demonstrate an understanding of inverses of relations.

• determine the equation of the inverse of a linear, quadratic, exponential, or logarithmic function and analyze its graph
• EXCELLENCE- determine restrictions on the domain of a function in order for its inverse to be a function, given the graph or equation

Specific Outcome 7

Demonstrate an understanding of logarithms.

• determine, without technology, the exact values of simple logarithmic expressions
• estimate the value of a logarithmic expression using benchmarks
• convert between y = b^x and log_by = x
• EXCELLENCE- convert with more than 2 steps.

Specific Outcome 8

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

• simplify and/or expand logarithmic expressions using the laws of logarithms

Specific Outcome 9

Graph and analyze exponential and logarithmic functions. VIDEO

• sketch and analyze (domain, range, intercepts, asymptote) the graphs of exponential or logarithmic functions and their transformations VIDEO

Specific Outcome 10

Solve problems that involve exponential and logarithmic equations.

• solve exponential equations that:
• –can be simplified to a common base
• –cannot be simplified to a common base and whose exponents are monomials
• EXCELLENCE- solve when equations cannot be simplified to a common base OR numerical coefficient
• Solve a logarithm and recognize extraneous solution.
• Solve real world problems and applications such as earthquake intensities.
• EXCELLENCE- Solve for exponent in comparison problems.

Specific Outcome 11

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

• identify whether a binomial is a factor of a given polynomial
• completely factor a polynomial of degree 3, 4, or 5

Specific Outcome 12

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

• identify and explain whether a given function is a polynomial function
• find the zeros of a polynomial function and explain their relationship to the x-intercepts of the graph and the roots of an equation
• sketch and analyze (in terms of multiplicities, y-intercept, domain and range, etc.) a polynomial function
• provide a partial solution to solve a problem by modelling a given situation with a polynomial function
• EXCELLENCE - Provide FULL solution.
• determine the equation of a polynomial function in factored form, given its graph and/or key characteristics

Specific Outcome 13

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

• sketch and analyze (in terms of domain, range, invariant points, x- and y-intercepts)
• find the zeros of a radical function graphically and explain their relationship to the x-intercepts of the graph and the roots of an equation

Specific Outcome 14

Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials, or trinomials).

• sketch and analyze (in terms of vertical asymptotes or point of discontinuity, domain, x- and y-intercepts) rational functions
• find the zeros of a rational function graphically and explain their relationship to the x-intercepts of the graph and the roots of an equation
• determine the equation of a rational function given its graph and/or key characteristics
• EXCELLENCE -determine the equation of a horizontal asymptote and the range of a rational function
• VIDEO
• EXCELLENCE -find the coordinates of the point of discontinuity of a rational function
• VIDEO
• EXCELLENCE- determine the equation of a rational function containing a point of discontinuity, given its graph and/or key characteristics
• VIDEO
• VIDEO (with hole)

Trigonometry

Specific Outcome 1

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

• demonstrate an understanding of the radian measure of an angle as a ratio of the subtended arc to the radius of a circle
• convert from radians to degrees and vice versa
• solve problems involving arc length, radius, and angle measure in either radians or degrees