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Math
Oklahoma Math
Algebra 1 (A1): Functions (F)
Distinguish between relations and functions.
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Identify the dependent variable, independent variable, domain and range given a function, equation, or graph. Identify restrictions on the domain and range in mathematical models.
- Determine the domain of functions
- Determining whether values are in domain of function
- Domain and range from graph
- Examples finding the domain of functions
- Function domain word problems
- Identifying values in the domain
- What is the domain of a function?
- What is the range of a function?
- Worked example: determining domain word problem (all integers)
- Worked example: determining domain word problem (positive integers)
- Worked example: determining domain word problem (real numbers)
- Worked example: domain and range from graph
Write linear functions, using function notation, to represent mathematical models.
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Read and interpret the linear piecewise function, given a graph modeling a situation.
- Evaluate piecewise functions
- Evaluate step functions
- Introduction to piecewise functions
- Piecewise functions graphs
- Solving equations graphically: word problems
- Worked example: domain & range of piecewise linear functions
- Worked example: domain & range of step function
- Worked example: evaluating piecewise functions
Interpret graphs as being discrete or continuous.
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Distinguish between linear and nonlinear (including exponential) functions. Understand that linear functions grow by equal intervals (arithmetic) and that exponential functions grow by equal factors over equal intervals (geometric).
- Exponential vs. linear models
- Exponential function graph
- Exponential vs. linear models: verbal
- Exponential vs. linear growth
- Exponential vs. linear growth
- Exponential vs. linear growth over time
- Exponential vs. linear growth over time
- Exponential vs. linear models: table
- Linear vs. exponential growth: from data
- Linear vs. exponential growth: from data
- Linear vs. exponential growth: from data (example 2)
- Warmup: exponential vs. linear growth
- Writing exponential functions from graphs
- Writing exponential functions from tables
Recognize the parent functions 𝑓(𝑥) = 𝑥 and 𝑓(𝑥) = |𝑥|. Predict the effects of vertical and horizontal transformations 𝑓(𝑥 + 𝑐) and 𝑓(𝑥) + 𝑐, algebraically and graphically.
- Absolute value graphs review
- Graph absolute value functions
- Graphing absolute value functions
- Reflect functions
- Scale & reflect absolute value graphs
- Scale functions vertically
- Scaling & reflecting absolute value functions: graph
- Shift absolute value graphs
- Shift functions
- Shifting absolute value graphs
- Shifting functions examples
- Shifting functions introduction
Identify and generate equivalent representations of linear functions, graphs, tables, and real-world situations.
Use function notation; evaluate a function, including nonlinear, at a given point in its domain algebraically and graphically. Interpret the results in terms of the original context.
- Composing functions
- Evaluate composite functions
- Evaluate composite functions: graphs & tables
- Evaluate function expressions
- Evaluate functions
- Evaluate functions from their graph
- Evaluating composite functions
- Evaluating composite functions (advanced)
- Evaluating composite functions: using graphs
- Evaluating composite functions: using tables
- Evaluating discrete functions
- Function inputs & outputs: equation
- Function inputs & outputs: graph
- Function notation word problem: bank
- Function notation word problem: beach
- Function notation word problems
- Intro to composing functions
- Worked example: evaluating expressions with function notation
- Worked example: matching an input to a function's output (equation)
- Worked example: matching an input to a function's output (graph)
- Worked example: two inputs with the same output (graph)
- Writing linear equations in all forms
Add, subtract, and multiply functions using function notation.