- standard
Understand the concept of a function and use function notation.
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Interpreting Functions
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined…
- standard
Understand the concept of a function and use function notation.
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Interpreting Functions
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
- standard
Understand the concept of a function and use function notation.
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Interpreting Functions
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the …
- standard
Represent and solve equations and inequalities graphically
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Reasoning with Equations and Inequalities
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution…
- standard
Represent and solve equations and inequalities graphically
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Reasoning with Equations and Inequalities
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); fi…
- standard
Represent and solve equations and inequalities graphically
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Reasoning with Equations and Inequalities
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could b…
- standard
Solve systems of equations
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Reasoning with Equations and Inequalities
(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
- standard
Solve systems of equations
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Reasoning with Equations and Inequalities
(+) Represent a system of linear equations as a single matrix equation in a vector variable.
- standard
Solve systems of equations
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Reasoning with Equations and Inequalities
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of …
- standard
Solve systems of equations
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Reasoning with Equations and Inequalities
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
- standard
Solve systems of equations
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Reasoning with Equations and Inequalities
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system …
- standard
Solve equations and inequalities in one variable
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Reasoning with Equations and Inequalities
Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate t…
- standard
Solve equations and inequalities in one variable
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Reasoning with Equations and Inequalities
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive…
- standard
Solve equations and inequalities in one variable
- 9th - 12th Grade
- Michigan State Math Standards
- Algebra: Reasoning with Equations and Inequalities
Solve quadratic equations in one variable.