- standard
Construct and compare linear, quadratic, and exponential models and solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Linear, Quadratic, and Exponential Models
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.*
- standard
Construct and compare linear, quadratic, and exponential models and solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Linear, Quadratic, and Exponential Models
Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.*
- standard
Construct and compare linear, quadratic, and exponential models and solve problems
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Linear, Quadratic, and Exponential Models
Distinguish between situations that can be modeled with linear functions and with exponential functions.*
- standard
Build new functions from existing functions
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Building Functions
(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
- standard
Build new functions from existing functions
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Building Functions
(+) Produce an invertible function from a non-invertible function by restricting the domain.
- standard
Build new functions from existing functions
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Building Functions
(+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
- standard
Build new functions from existing functions
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Building Functions
(+) Verify by composition that one function is the inverse of another.
- standard
Build new functions from existing functions
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Building Functions
Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2(x^3) or f(x) =…
- standard
Build new functions from existing functions
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Building Functions
Find inverse functions.
- standard
Build new functions from existing functions
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Building Functions
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the val…
- standard
Build a function that models a relationship between two quantities
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Building Functions
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*
- standard
Build a function that models a relationship between two quantities
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Building Functions
(+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a func…
- standard
Build a function that models a relationship between two quantities
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Building Functions
Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant f…
- standard
Build a function that models a relationship between two quantities
- 9th - 12th Grade
- Michigan State Math Standards
- Functions: Building Functions
Determine an explicit expression, a recursive process, or steps for calculation from a context.