ALEX Resources

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Learning Activities (1) Building blocks of a lesson plan that include before, during, and after strategies to actively engage students in learning a concept or skill. Classroom Resources (3)


ALEX Learning Activities  
   View Standards     Standard(s): [MA2019] AL1-19 (9-12) 23 :
23. Identify the effect on the graph of replacing f(x) by f(x)+k,k·f(x), f(k·x), 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 explain the effects on the graph, using technology as appropriate. Limit to linear, quadratic, exponential, absolute value, and linear piecewise functions.
[MA2015] AL2 (9-12) 34 :
34 ) 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. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [F-BF3]

[MA2015] ALT (9-12) 34 :
34 ) 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. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [F-BF3]

Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Let's Experiment With Graphs of Functions Using Technology!
Description:

This learning activity Let's Experiment With Graphs of Functions Using Technology! will be used during a lesson on identifying 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 using technology, finding the value of k given the graphs, and recognizing even and odd functions from their graphs and algebraic expressions for them.

This activity results from the ALEX Resource Development Summit.




ALEX Learning Activities: 1

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ALEX Classroom Resources  
   View Standards     Standard(s): [MA2015] AL2 (9-12) 35 :
35 ) Find inverse functions. [F-BF4]

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. [F-BF4a]

Example: f(x) =2x3 or f(x) = (x+1)/(x-1) for x ≠ 1.

[MA2015] AL2 (9-12) 29 :
29 ) Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [F-IF5]

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.

[MA2015] AL2 (9-12) 36 :
36 ) For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers, and the base b is 2, 10, or e; evaluate the logarithm using technology. [F-LE4]

[MA2019] AL1-19 (9-12) 17 :
17. Combine different types of standard functions to write, evaluate, and interpret functions in context. Limit to linear, quadratic, exponential, and absolute value functions.

a. Use arithmetic operations to combine different types of standard functions to write and evaluate functions.

Example: Given two functions, one representing flow rate of water and the other representing evaporation of that water, combine the two functions to determine the amount of water in a container at a given time.

b. Use function composition to combine different types of standard functions to write and evaluate functions.

Example: Given the following relationships, determine what the expression S(T(t)) represents.

Function Input Output
G Amount of studying: s Grade in course: G(s)
S Grade in course: g Amount of screen time: S(g)
T Amount of screen time: t Number of follers: T(t)
[MA2019] AL1-19 (9-12) 23 :
23. Identify the effect on the graph of replacing f(x) by f(x)+k,k·f(x), f(k·x), 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 explain the effects on the graph, using technology as appropriate. Limit to linear, quadratic, exponential, absolute value, and linear piecewise functions.
[MA2019] AL1-19 (9-12) 30 :
30. 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 piecewise-defined functions, including step functions and absolute value functions.

c. Graph exponential functions, showing intercepts and end behavior.
Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Algebra II Module 3, Topic C: Exponential and Logarithmic Functions and Their Graphs
URL: https://www.engageny.org/resource/algebra-ii-module-3-topic-c-overview
Description:

In Module 3, Topic C, students graph logarithmic functions, identifying key features (F-IF.4, F-IF.7) and discover how the logarithmic properties are evidenced in the graphs of corresponding logarithmic functions. The inverse relationship between an exponential function and its corresponding logarithmic function is made explicit (F-BF.3).  In the final lesson in Topic C, students synthesize what they know about linear, quadratic, sinusoidal, and exponential functions to determine which function is most appropriate to use to model a variety of real-world scenarios (F-BF.1a).



   View Standards     Standard(s): [MA2015] AL1 (9-12) 16 :
16 ) Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. [A-REI1]

[MA2019] AL1-19 (9-12) 23 :
23. Identify the effect on the graph of replacing f(x) by f(x)+k,k·f(x), f(k·x), 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 explain the effects on the graph, using technology as appropriate. Limit to linear, quadratic, exponential, absolute value, and linear piecewise functions.
[MA2019] AL1-19 (9-12) 30 :
30. 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 piecewise-defined functions, including step functions and absolute value functions.

c. Graph exponential functions, showing intercepts and end behavior.
Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Algebra I Module 3, Topic C: Transformations of Functions
URL: https://www.engageny.org/resource/algebra-i-module-3-topic-c-overview
Description:

In Module 3, Topic C, students extend their understanding of piecewise functions and their graphs including the absolute value and step functions. They learn a graphical approach to circumventing complex algebraic solutions to equations in one variable, seeing them as f(x) = g(x) and recognizing that the intersection of the graphs of f(x) and g(x) are solutions to the original equation (A-REI.D.11). Students use the absolute value function and other piecewise functions to investigate transformations of functions and draw formal conclusions about the effects of a transformation on the function’s graph (F-IF.C.7, F-BF.B.3).



   View Standards     Standard(s): [MA2019] AL1-19 (9-12) 12 :
12. Create equations in two or more variables to represent relationships between quantities in context; graph equations on coordinate axes with labels and scales and use them to make predictions. Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions.
[MA2019] AL1-19 (9-12) 23 :
23. Identify the effect on the graph of replacing f(x) by f(x)+k,k·f(x), f(k·x), 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 explain the effects on the graph, using technology as appropriate. Limit to linear, quadratic, exponential, absolute value, and linear piecewise functions.
[MA2019] AL1-19 (9-12) 29 :
29. 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. Limit to linear, quadratic, exponential, and absolute value functions.
[MA2019] AL1-19 (9-12) 30 :
30. 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 piecewise-defined functions, including step functions and absolute value functions.

c. Graph exponential functions, showing intercepts and end behavior.
Subject: Mathematics (9 - 12)
Title: Algebra I Module 4, Topic C: Function Transformations and Modeling
URL: https://www.engageny.org/resource/algebra-i-module-4-topic-c-overview
Description:

In Module 4, Topic C, students explore the families of functions that are related to the parent functions, specifically for quadratic (f(x) = x2), square root (f(x) = the square root of x), and cube root (f(x) = cube root of x), to perform horizontal and vertical translations as well as shrinking and stretching (F-IF.C.7b, F-BF.B.3). They recognize the application of transformations in vertex form for a quadratic function and use it to expand their ability to efficiently sketch graphs of square and cube root functions. Students compare quadratic, square root, or cube root functions in context and represent each in different ways (verbally with a description, as a table of values, algebraically, or graphically). In the final two lessons, students examine real-world problems of quadratic relationships presented as a data set, a graph, a written relationship, or an equation. They choose the most useful form for writing the function and apply the techniques learned throughout the module to analyze and solve a given problem (A-CED.A.2), including calculating and interpreting the rate of change for the function over an interval (F-IF.B.6).



ALEX Classroom Resources: 3

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