MCR3UR: Functions and Transformations SAMPLE Name: ______

Sept 23, 2014Time: 75 min

Instructions:

Carefully read each problem and then provide complete responses with justificationsand explanationsusingmultiple representations (algebraic, numerical, graphical, etc). Your solutions must be independent of your graphing calculator.

Evaluation:

Code / Questions / Criteria / Level
A1 / ALL / Demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations
-- / ALL / Communication

ric:

Criteria / 50-59%
(Level 1) / 60-69%
(Level 2) / 70-79%
(Level 3) / 80-100%
(Level 4)
Knowledge and Understanding: Content Knowledge and comprehension of meaning and significance
Understanding of mathematical concepts / Demonstrates limitedunderstanding of concepts / Demonstrates some understanding of concepts / Demonstrates considerable understanding of concepts / Demonstrates thorough understanding of concepts
Application: The use of knowledge and skills to make connections within and between various contexts
Selects and uses tools and strategies to solve problems / Selects and applies appropriate tools and strategies with major errors, omissions, or mis-sequencing / Selects and applies appropriate tools and strategies with minor errors, omissions, or mis-sequencing / Selects and applies appropriate tools and strategies accurately, and in a logical sequence / Selects and applies appropriate and efficient tools strategies accurately to create mathematically elegant solutions
Thinking: The use of critical and creating thinking skills and / or processes
Uses critical thinking skills to solve a problem / Uses minimal logic and precision in mathematical reasoning to solve problems / Uses logic to solve problems but lacks precision in mathematical reasoning / Solves problems logically and with precision in mathematical reasoning / Demonstrates a sophisticated level of mathematical reasoning and precision in solving problems
Communication: The conveying of meaning through various forms
Expression and organization of mathematical thinking and ideas using oral, visual and written forms / Expresses and organizes mathematical thinking with limited effectiveness / Expresses and organizes mathematical thinking with some effectiveness / Expresses and organizes mathematical thinking with considerable effectiveness / Expresses and organizes mathematical thinking with a high degree of effectiveness

MCR3UR: Functions and Transformations (SAMPLE) Name: ______

  1. Which of the following mapping diagrams represent functions? Clearly explain your reasoning. Which are invertible?
  1. A runner’s distance from home (in km) at time t (in hrs) is represented by the function d(t)= -t2 + 3t +10.
  2. Determine how far the runner is from home at 4 hours.
  3. Determine when the runner will return home.

  1. Create the I/O diagram to match the following equations.Describe what transformations have been applied to the parent function and in what order those transformations occurred.
  2. b.
  1. Determine the domain and range for the function in question 3a.
  1. Determine the equation of the inverse of . NOTE: This is the same function as in question 3a.

  1. Match each of the following equations with its graph.
  1. Create a rough sketch of the following function and its parent function.Explain your reasoning

  1. A function has had the following transformations applied to it in the order below. Determine the equation of the new function.

-A vertical stretch by a factor of 7

-A horizontal translation 2 units to the left

-A vertical translation down by 5 units.

-A horizontal stretch by a factor of 3

  1. Consider the graph shown below. On the same set of axes sketch it’s inverse.Explain your reasoning.

  1. The points (1, 1) and (2,-1) have been transformed into the points (4,-3) and (7,1) respectively by the same set of transformations. Determine what transformations have occurred.

  1. The graph below shows a function,, that has been transformed from the parent function . Determine the equation of the equation of.