Includes Standard Clusters:

• Extend the properties of exponents to rational exponents.
• Solve systems of equations.
• Represent and solve equations and inequalities graphically.
• Understand the concept of a function and use function notation.
• Interpret functions that arise in applications in terms of a context.
• Analyze functions using different representations.
• Build a function that models a relationship between two quantities.
• Build new functions from existing functions.
• Construct and compare linear, quadratic, and exponential models and solve problems.
• Interpret expressions for functions in terms of the situation they model.

## Collection Contents

### Cluster - Extend the properties of exponents to rational exponents.

by Allen Wolmer

In implementing the standards in curriculum, these standards should occur before discussing exponential functions with continuous domains.Includes Standards N.RN.1, N.RN.2
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### Cluster - Solve systems of equations.

by Allen Wolmer

Build on student experiences graphing and solving systems of linear equations from middle school to focus on justification of the methods used. Include cases where the two equations describe the same line (yielding infinitely many solutions) and cases where two equations describe parallel lines (yielding no solution); connect to GPE.5 when it is taught in Geometry, which requires students to prove the slope criteria for parallel lines.
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### Cluster - Represent and solve equations and inequalities graphically.

by Allen Wolmer

For A.REI.10, focus on linear and exponential equations and be able to adapt and apply that learning to other types of equations in future courses. For A.REI.11, focus on cases where f and g are linear or exponential.
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### Cluster - Understand the concept of a function and use function notation.

by Allen Wolmer

Students should experience a variety of types of situations modeled by functions. Detailed analysis of any particular class of functions at this stage is not advised. Students should apply these concepts throughout their future mathematics courses.Draw examples from linear and exponential functions. In F.IF.3, draw connection to F.BF.2, which requires students to write arithmetic and geometric sequences. Emphasize arithmetic and geometric sequences as examples of linear and exponential functions.
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### Cluster - Interpret functions that arise in applications in terms of a context.

by Allen Wolmer

For F.IF.4 and 5, focus on linear and exponential functions. For F.IF.6, focus on linear functions and exponential functions whose domain is a subset of the integers. Unit 5 in this course and the Algebra II course address other types of functions.
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### Cluster - Analyze functions using different representations.

by Allen Wolmer

For F.IF.7a, 7e, and 9 focus on linear and exponentials functions. Include comparisons of two functions presented algebraically. For example, compare the growth of two linear functions, or two exponential functions such as y=3^n and y=100^2
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### Cluster - Build a function that models a relationship between two quantities.

by Allen Wolmer

Limit to F.BF.1a, 1b, and 2 to linear and exponential functions. In F.BF.2, connect arithmetic sequences to linear functions and geometric sequences to exponential functions.
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### Cluster - Build new functions from existing functions.

by Allen Wolmer

Focus on vertical translations of graphs of linear and exponential functions. Relate the vertical translation of a linear function to its y-intercept. While applying other transformations to a linear graph is appropriate at this level, it may be difficult for students to identify or distinguish between the effects of the other transformations included in this standard.
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### Cluster - Construct and compare linear, quadratic, and exponential models and solve problems.

by Allen Wolmer

For F.LE.3, limit to comparisons between linear and exponential models. In constructing linear functions in F.LE.2, draw on and consolidate previous work in Grade 8 on finding equations for lines and linear functions (8.EE.6, 8.F.4).
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### Cluster - Interpret expressions for functions in terms of the situation they model

by Allen Wolmer

Limit exponential functions to those of the form f = b^x + k.
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