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Algebra 2 2019
Functions
1.2 Explore inverse functions (and compositions)
CCSS 4 – Mastery 3 – Proficient 2 - Basic 1 – Below Basic
0 – No Evidence Produce inverse functions (F.BF.4)
Can extend thinking beyond the standard, including tasks that may involve one of the following:
- Designing
- Connecting
- Synthesizing
- Applying
- Justifying
- Critiquing
- Analyzing
- Creating
- Proving
Can do all of the following:
- Read values of an inverse function from a graph and table
- Given a simple function, find its inverse
- Compose functions to verify if one function is the inverse of another function
Can do 2 of the following:
- Read values of an inverse function from a graph and table
- Given a simple function, find its inverse
- Compose functions to verify if one function is the inverse of another function
Can do 1 of the following:
- Read values of an inverse function from a graph and table
- Given a simple function, find its inverse
- Compose functions to verify if one function is the inverse of another function
Little evidence of reasoning or application to solve the problem
Does not meet the criteria in a level 1
Evaluate composed functions (F.BF.1c)
Evaluate the composition of 2 functions in context of a situation
Evaluate the composition of 2 functions
Evaluate a function for a given value and use that result to evaluate a second function
F.BF.4 Find inverse functions. a. (+)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 x3 or f(x) = (x+1)/(x-1) for x ≠ 1. b. (+) Verify by composition that one function is the inverse of another. c. (+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
F.BF.1c Write a function that describes a relationship between two quantities. c. (+) 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 function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
Algebra 2 2019
Functions
1.3 Explore function transformations
CCSS 4 – Mastery 3 – Proficient 2 - Basic 1 – Below Basic
0 – No Evidence Identify transform- ations and key features of graphs (F.IF.7a/b, F.BF.3)
Can extend thinking beyond the standard, including tasks that may involve one of the following:
- Designing
- Connecting
- Synthesizing
- Applying
- Justifying
- Critiquing
- Analyzing
- Creating
- Proving
Identify the effect on a graph by replacing f(x) with more than two transformations: f ( x ) + k , a f ( x ), f ( bx ), f ( x + h ) for specific positive and negative values of the constants a, b, h, and k
Write a function given more than two transformations.
Graph function transformations (quadratics, square root, cube root, linear, absolute value) and identify all related key features of a graph in context of a situation. ● lines of symmetry ● intercepts ● domain/range
Identify the effect on a graph by replacing f(x) with two transformations: f ( x ) + k , a f ( x ), f ( bx ), f ( x + h ) for specific positive and negative values of the constants a, b, h, and k
Write a function given two transformations.
Graph function transformations (quadratics, square root, cube root, linear, absolute value) and identify all related key features of a graph. ● lines of symmetry ● intercepts ● domain/range
Identify the effect on a graph by replacing f(x) with a single transformation: f ( x ) + k , a f ( x ), f ( bx ), f ( x + h ) for specific positive and negative values of the constants a, b, h, and k
Write a function given a transformation.
Given the graphs of functions (quadratics, square root, cube root, linear, absolute value) identify all related key features of a graph. ● lines of symmetry ● intercepts ● domain/range
Little evidence of reasoning or application to solve the problem
Does not meet the criteria in a level 1
F.IF.7a/b Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
F.BF.3 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 value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
