- x-axis
- y-axis
- line $y=x$.
| (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. |
