4.5

Topic

Implicitly Defined Functions

Practice by unit: Functions Involving Parameters, Vectors, and Matrices

Sub-standards

• 4.5.A.1 — Construct a graph of an equation involving two variables. An equation involving two variables can implicitly describe one or more functions.
• 4.5.A.2 — An equation involving two variables can be graphed by finding solutions to the equation.
• 4.5.A.3 — Solving for one of the variables in an equation involving two variables can define a function whose graph is part or all of the graph of the equation.
• 4.5.B.1 — Determine how the two quantities related in an implicitly defined function vary together. For ordered pairs on the graph of an implicitly defined function that are close together, if the ratio of the change in the two variables is positive, then the two variables simultaneously increase or both decrease; conversely, if the ratio is negative, then a
• 4.5.B.2 — The rate of change of x with respect to y or of y with respect to x can be zero, indicating vertical or horizontal intervals, respectively. UNIT 4 Additional Topic Available to Schools )2 ) 2 (x h − ( y k − + = 1 2 b 2a )2 (x h − y k − − = 1 2 b 2a ) 2 ( y k − )2 (x h − − = 1 2 b 2 a b y k − = ± − (x h). a