Mathematics | Course : Model Algebra I (Traditional Pathway)
Domain - Building Functions
Cluster - Build a function that models a relationship between two quantities.
[AI.F-BF.A.1] - Write linear, quadratic, and exponential functions that describe a relationship between two quantities.*
- Exponential function
A function of the form y = a •bx where a > 0 and either 0 < b < 1 or b > 1. The variables do not have to be x and y. For example, A = 3.2 • (1.02)t is an exponential function. - Linear function
A function with an equation of the form y = mx + b, where m and b are constants - Quadratic function
A function that can be represented by an equation of the form y = ax2 + bx + c, where a, b, and c are arbitrary, but fixed, numbers and a 0. The graph of this function is a parabola.
[AI.F-IF.A.1] -
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 range. If f is a function and x is an element of its domain, then f(x) denotes the output (range) of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
[AI.F-LE.A.2] -
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (including reading these from a table).*
[HS.ESS.1.1] -
Use informational text to explain that the life span of the Sun over approximately 10 billion years is a function of nuclear fusion in its core. Communicate that stars, through nuclear fusion over their life cycle, produce elements from helium to iron and release energy that eventually reaches Earth in the form of radiation. State Assessment Boundary: Specific stages of the life of a star, details of the many different nucleosynthesis pathways for stars of differing masses, or calculations of energy released are not expected in state assessment.
[HS.LS.1.4] -
Construct an explanation using evidence for why the cell cycle is necessary for the growth, maintenance, and repair of multicellular organisms. Model the major events of the cell cycle, including (a) cell growth and DNA replication, (b) separation of chromosomes (mitosis), and (c) separation of cell contents. State Assessment Boundary: Specific gene control mechanisms or specific details of each event (e.g., phases of mitosis) are not expected in state assessment.