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Common Core: Standard
Common Core: ELA
Common Core: Math
CCLS - Math: F.BF.3
- Building Functions
- Build New Functions From Existing Functions
- State Standard:
- 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.
- Student Outcomes Students study transformations of the graphs of logarithmic functions. Students use the properties of logarithms and exponents to produce equivalent forms of exponential and...
- In 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...
- Exponential and Logarithmic Functions In this module, students synthesize and generalize what they have learned about a variety of function families. They extend the domain of exponential functions...
- In 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...
- In 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...
- Student Outcomes Students compare two different quadratic, square root, or cube root functions represented as graphs, tables, or equations. They interpret, contextualize and abstract various...
- Student Outcomes Students make a connection between the symbolic and graphic forms of quadratic equations in the completed-square (vertex) form. They efficiently sketch a graph of a quadratic...
- Student Outcomes Students recognize and use parent functions for absolute value, quadratic, square root, and cube root to perform transformations that stretch and shrink the graphs of the functions...
- Student Outcomes Students recognize and use parent functions for linear, absolute value, quadratic, square root, and cube root to perform vertical and horizontal translations. They identify how the...
- Student Outcomes Students apply their understanding of transformations of functions and their graphs to piecewise functions.
- Student Outcomes Students examine that a horizontal scaling with scale factor k of the graph of y = f(x) corresponds to changing the equation from y = f(x) to y = f[(1/k)(x)].
- Student Outcomes Students examine that a horizontal translation of the graph of y = f(x) corresponds to changing the equation from y = f(x) to y = f(x - k).
- Student Outcomes Students examine that a vertical translation of the graph of y = f(x) corresponds to changing the equation from y = f(x) to y = f(x) + k. Students examine that a vertical scaling of...
- Algebra I Module 4: Polynomial and Quadratic Expressions, Equations, and Functions In earlier modules, students analyze the process of solving equations and developing fluency in writing,...
- Algebra I Module 3: Linear and Exponential Functions In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module,...