Understand the concept of a function and use function notation
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 of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
2 - Understand (function from one set [domain] to another set [range] assigns to each domain element exactly one range element)
|
2 - I can understand that a function from one set [domain] to another set [range] assigns to each domain element exactly one range element.
|
A. The set of numbers that makes up the domain is the set of inputs for the function.
B. The set of numbers that makes up the range is the set of outputs for the function.
|
A.1 What is the domain of a function?
B.1 What is the range of a function?
|
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
3 - Use (function notation)
2 - Evaluate (functions for inputs in their domains)
2 - Interpret (statements using function notation in terms of a context)
|
3 - I can use function notation.
2 - I can evaluate functions for inputs in their domains.
2 - I can interpret statements that use function notation in terms of a context.
|
A. Function notation allows one to name a function and indicate the variable being used as its domain.
|
A.1 Why is function notation important?
|
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Functions
|
1 - Recognize (sequences are functions)
1 - Recognize (sequences are sometimes defined recursively)
1 - Recognize (domain is a subset of the integers)
|
1 - I can recognize that sequences are functions.
1 - I can recognize that sequences are sometimes defined recursively.
1 - I can recognize that the domain is a subset of the integers.
|
A. Sequences are functions.
|
A.1 What is a sequence?
|
Interpret functions that arise in applications in terms of the context
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
2 - Interpret (key features of a graph for functions that model a relationship between 2 quantities)
2 - Interpret (key features of tables for functions that model a relationship between 2 quantities)
3 - Sketch (graphs showing key features given verbal descriptions of the relationship)
|
2 - I can interpret key features of a graph for a function that models a relationship between 2 quantities.
2 - I can interpret key features of a table for a function that models a relationship between 2 quantities.
3 - I can sketch graphs showing key features given a verbal description of the relationship.
|
A. Functions can be shown in a table or a graph.
|
A.1 How can a table or a graph represent a function?
|
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Functions
|
1 - Relate (function's domain to its graph)
1 - Relate (function's domain to the quantitative relationship it describes)
|
1 - I can relate the domain of a function to its graph.
1 - I can relate the domain of a function to the quantitative relationship it describes.
|
A. The domain of a function may have specific meaning in the context of a problem.
|
A.1 What is the meaning of the domain in a problem?
|
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
2 - Calculate (average rate of change of a function presented symbolically over a specified interval)
2 - Calculate (average rate of change of a function presented as a table over a specified interval)
2 - Interpret (average rate of change of a function presented symbolically over a specified interval)
2 - Interpret (the average rate of change of a function presented as a table over a specified interval)
3 - Estimate (the rate of change from a graph)
|
2 - I can calculate the average rate of change of a function presented symbolically over a specified interval.
2 - I can calculate the average rate of change of a function presented as a table over a specified interval.
2 - I can interpret the average rate of change of a function presented symbolically over a specified interval.
2 - I can interpret the average rate of change of a function presented as a table over a specified interval.
3 - I can estimate the rate of change from a graph.
|
A. One can calculate the average rate of change of a function from different representations.
|
A.1 How do I find the average rate of change of a function?
|
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Functions
Function graphs [a]
Function graphs [b]
Function graphs [c]
Function graphs [d]
Function graphs [e]
|
3 - Graph (functions expressed symbolically)
1 - Show (key features of the graph)
3 - Graph (by hand in simple cases)
3 - Use (technology for complicated cases)
3 - Graph (linear functions [a])
3 - Graph (quadratic functions [a])
2 - Show (intercepts, maxima, and minima [a])
3 - Graph (square root functions [b])
3 - Graph (cube root functions [b])
3 - Graph (piece-wise functions [b])
3 - Graph (step functions [b])
3 - Graph (absolute value functions [b])
3 - Graph (polynomial functions [c])
2 - Identify (zeros [c])
2 - Show (end behavior [c])
3 - Graph (rational functions [d])
2 - Identify (zeros and asymptotes [d])
2 - Show (end behavior [d])
3 - Graph (exponential functions [e])
3 - Graph (logarithmic functions [e])
2 - Show (intercepts and end behavior [e])
3 - Graph (trigonometric functions [e])
2 - Show (period, midline, and amplitude [e])
|
3 - I can graph functions expressed symbolically.
1 - I can show key features of the graph.
3 - I can graph by hand in simple cases.
3 - I can use technology for complicated cases.
3 - I can graph linear functions [a].
3 - I can graph quadratic functions [a].
2 - I can show intercepts, maxima, and minima [a].
3 - I can graph square root functions [b].
3 - I can graph cube root functions [b].
3 - I can graph piece-wise functions [b].
3 - I can graph step functions [b].
3 - I can graph absolute value functions [b].
3 - I can graph polynomial functions [c].
2 - I can identify zeros [c].
2 - I can show end behavior [c].
3 - I can graph rational functions [d].
2 - I can identify zeros and asymptotes [d].
2 - I can show end behavior [d].
3 - I can graph exponential functions [e].
3 - I can graph logarithmic functions [e].
2 - I can show intercepts and end behavior [e].
3 - I can graph trigonometric functions [e].
2 - I can show period, midline, and amplitude [e].
|
A. One can use technology to graph complicated functions.
B. Each type of function graph has its own key features.
C. The key features of a function's graph are often used when problem solving.
D. The key features of a function's graph along with basic knowledge of the behavior of the graph aids in graph sketching.
|
A.1 Do I always have to graph functions by hand?
A.2 Can I find the key features of a graph if I use technology?
B.1 How do I identify the key features of a graph?
C.1 Why do I need to identify the key features of a graph?
D.1 How do I sketch the graph of a function by hand?
|
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Quadratic functions [a]
Properties of exponents [b]
|
2 - Write (functions defined by an expression in different but equivalent forms)
2 - Explain (different properties of the function)
3 - Use (factoring [a])
3 - Use (completing the square [a])
2 - Show (zeros, extreme values, and symmetry of graph [a])
2 - Interpret (in terms of context [a])
3 - Use (properties of exponents [b])
2 - Interpret (expressions for exponential functions [b])
|
2 - I can write a function defined by an expression in different but equivalent forms.
2 - I can explain different properties of the function.
3 - I can use factoring [a].
3 - I can use completing the square [a].
2 - I can show zeros, extreme values, and symmetry of graph [a].
2 - I can interpret in terms of context [a].
3 - I can use properties of exponents [b].
2 - I can interpret expressions for exponential functions [b].
|
A. Functions can be defined by expressions as well as graphs and tables.
B. Key features of a function may be found graphically or algebraically.
C. There is often more than one way to algebraically find key features of a function.
|
A.1 Why would I need to change the representation of a function?
B.1 Do I have to graph a function to find its key features?
C.1 How can I find key features algebraically?
|
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Functions
|
2 - Compare (properties of 2 functions each represented in a different way)
|
2 - I can compare properties of 2 functions each represented in a different way
|
A. One can compare functions regardless of form of representation.
|
A.1 How do I compare functions if they are not of the same form?
|
Be the first to comment below.
Please enter a Registration Key to continue.