P30.8
Demonstrate understanding of functions, relations, inverses and their related equations resulting from reflections through the:
  • x-axis
  • y-axis
  • line $y=x$.
Indicators for this outcome
(a)

Generalize and apply 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 $y=x$.

(b)

Develop and apply strategies for sketching the reflection of a function $y = f(x)$ through the x-axis, the y-axis, or the line $y=x$ when the graph of $f(x)$ is given but the equation is not.

(c)

Develop and apply strategies for sketching the graphs of $y=-f(x)$, $y=f(-x)$, and $x=-f(y)$ when the graph of $f(x)$ is given and the equation is not.

(d)

Develop and apply strategies for writing the equation of a function that is the reflection of the function $f(x)$ through the x-axis, y-axis, or line $y=x$.

(e)

Develop and apply strategies for sketching the inverse of a relation, including reflection across the line $y=x$ and the transformation $(x,y)⇒(y,x)$.

(f)

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

(g)

Develop, generalize, explain, and apply strategies for determining if one or both of a relation and its inverse are functions.

(h)

Determine what restrictions must be placed on the domain of a function for its inverse to be a function.

(i)

Critique statements such as "If a relation is not a function, then its inverse also will not be a function".

(j)

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

(k)

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

(l)

Develop and apply numeric, algebraic, and graphic strategies to determine if two relations are inverses of each other.

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R054350
McGraw-Hill Ryerson Pre-Calculus 12. Student Edition
The student text consists of four units. Each unit opens with a two-page spread. The first page introduces what the students will learn throughout the unit and the second page introduces the unit project. Throughout the chapters are project corner boxes that will assist students to gather information for their projects. Each unit culminates with the project wrap-up. The chapters include career information based on the skills that will be learned. Opportunities are provided for students to make connections between math and the real world or to make connections to what students already know or may be studying in other classes. The student resource includes a table of contents, an answer key, a glossary and an index.
(More information)
•  McGraw-Hill Ryerson Pre-Calculus 12. Interactive Student Resource DVD
•  McGraw-Hill Ryerson Pre-Calculus 12. Interactive Teacher's Resource DVD
•  McGraw-Hill Ryerson Pre-Calculus 12. Teacher's Resource (Print & CD-ROM)
•  McGraw-Hill Ryerson Pre-Calculus 12. Teacher's Resource Package (Print, CD-ROM, Interactive Teacher's Resource DVD)
Media and Formats : Book
Price : $81.29
Record posted/updated: August 13, 2019