Mathematics 15. Define a function as a mapping from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range.
a. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Note: If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x.
b. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Limit to linear, quadratic, exponential, and absolute value functions.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given input/output relations between two variables in graphical form, verbal description, set of ordered pairs, or algebraic model, distinguish between those that are functions and non-functions. Using functional notation,
Evaluate functions for inputs.
Interpret statements in terms of context. Given a contextual relationship that may be represented as a function,
Determine that exactly one element of the range (output) is assigned to each element of the domain (input) by the function.
Relate the domain to its graph and to the quantitative relationship it describes. Teacher Vocabulary:
Domain
Range Function Relation
Function notation
Set notation Knowledge:
Students know:
Distinguishing characteristics of functions.
Conventions of function notation.
In graphing functions the ordered pairs are (x,f(x)) and the graph is y = f(x). Skills:
Students are able to:
Evaluate functions for inputs in their domains. Interpret statements that use function notation in terms of context. Accurately graph functions when given function notation.
Accurately determine domain and range values from function notation. Understanding:
Students understand that:
A function is a mapping of the domain to the rangeFunction notation is useful in contextual situations to see the relationship between two variables when the unique output for each input relation is satisfied. Diverse Learning Needs:
Essential Skills:
Learning Objectives: ALGI.15.1: Define domain, range, relation, function, table of values, input, and output.
ALGI.15.2: Understand the graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
ALGI.15.3: Understand that a function is a rule that assigns to each input exactly one output.
ALGI.15.4: Identify the equation of a function, given its graph.
ALGI.15.5: Find the range of a function given its domain.
ALGI.15.6: Recognize that f(x) and y are the same.
ALGI.15.7: Recall how to complete input/output tables.
ALGI.15.8: Recall how to read/interpret information from a table.
ALGI.15.9: Define function notation.
ALGI.15.10: Translate a simple word problem into function notation.
ALGI.15.11: Evaluate function when given x-value.
Prior Knowledge Skills:
Analyze the graph to determine the rate of change.
Generate the slope of a line using given ordered pairs.
Define linear functions, nonlinear functions, slope, and y-intercept
Identify ordered pairs.
Plot points on a coordinate plane., then connect points for the vertices to sketch a polygon.
Alabama Alternate Achievement Standards
AAS Standard:
