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912.F.IF.7c 
12 
Functions 
Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. 


912.F.IF.7d 
9 
Functions 
Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. 


912.F.IF.7d 
10 
Functions 
Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. 


912.F.IF.7d 
11 
Functions 
Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. 


912.F.IF.7d 
12 
Functions 
Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. 


912.F.IF.7e 
9 
Functions 
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 


912.F.IF.7e 
10 
Functions 
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 


912.F.IF.7e 
11 
Functions 
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 


912.F.IF.7e 
12 
Functions 
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. 


912.F.IF.8 
9 
Functions 
Analyze functions using different representations. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 


912.F.IF.8 
10 
Functions 
Analyze functions using different representations. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 


912.F.IF.8 
11 
Functions 
Analyze functions using different representations. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 


912.F.IF.8 
12 
Functions 
Analyze functions using different representations. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 


912.F.IF.8a 
9 
Functions 
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. 


912.F.IF.8a 
10 
Functions 
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. 


912.F.IF.8a 
11 
Functions 
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. 


912.F.IF.8a 
12 
Functions 
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. 


912.F.IF.8b 
9 
Functions 
Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponential growth and decay. 


912.F.IF.8b 
10 
Functions 
Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponential growth and decay. 


912.F.IF.8b 
11 
Functions 
Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponential growth and decay. 


912.F.IF.8b 
12 
Functions 
Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponential growth and decay. 


912.F.IF.9 
9 
Functions 
Analyze functions using different representations. 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. 


912.F.IF.9 
10 
Functions 
Analyze functions using different representations. 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. 


912.F.IF.9 
11 
Functions 
Analyze functions using different representations. 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. 


912.F.IF.9 
12 
Functions 
Analyze functions using different representations. 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. 


912.F.BF.1 
9 
Functions 
Build a function that models a relationship between two quantities. Write a function that describes a relationship between two quantities. 


912.F.BF.1 
10 
Functions 
Build a function that models a relationship between two quantities. Write a function that describes a relationship between two quantities. 


912.F.BF.1 
11 
Functions 
Build a function that models a relationship between two quantities. Write a function that describes a relationship between two quantities. 


912.F.BF.1 
12 
Functions 
Build a function that models a relationship between two quantities. Write a function that describes a relationship between two quantities. 


912.F.BF.1a 
9 
Functions 
Determine an explicit expression, a recursive process, or steps for calculation from a context. 


912.F.BF.1a 
10 
Functions 
Determine an explicit expression, a recursive process, or steps for calculation from a context. 


912.F.BF.1a 
11 
Functions 
Determine an explicit expression, a recursive process, or steps for calculation from a context. 


912.F.BF.1a 
12 
Functions 
Determine an explicit expression, a recursive process, or steps for calculation from a context. 


912.F.BF.1b 
9 
Functions 
Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 


912.F.BF.1b 
10 
Functions 
Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 


912.F.BF.1b 
11 
Functions 
Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 


912.F.BF.1b 
12 
Functions 
Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 


912.F.BF.1c 
9 
Functions 
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. 


912.F.BF.1c 
10 
Functions 
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. 


912.F.BF.1c 
11 
Functions 
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. 


912.F.BF.1c 
12 
Functions 
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. 


912.F.BF.2 
9 
Functions 
Build a function that models a relationship between two quantities. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 


912.F.BF.2 
10 
Functions 
Build a function that models a relationship between two quantities. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 


912.F.BF.2 
11 
Functions 
Build a function that models a relationship between two quantities. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 


912.F.BF.2 
12 
Functions 
Build a function that models a relationship between two quantities. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. 


912.F.BF.3 
9 
Functions 
Build new functions from existing functions. 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. 


912.F.BF.3 
10 
Functions 
Build new functions from existing functions. 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. 


912.F.BF.3 
11 
Functions 
Build new functions from existing functions. 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. 


912.F.BF.3 
12 
Functions 
Build new functions from existing functions. 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. 


912.F.BF.4 
9 
Functions 
Build new functions from existing functions. Find inverse functions. 


912.F.BF.4 
10 
Functions 
Build new functions from existing functions. Find inverse functions. 


912.F.BF.4 
11 
Functions 
Build new functions from existing functions. Find inverse functions. 


912.F.BF.4 
12 
Functions 
Build new functions from existing functions. Find inverse functions. 


912.F.BF.4a 
9 
Functions 
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(x^3) or f(x) = (x+1)/(x1) for x ? 1 (x not equal to 1). 


912.F.BF.4a 
10 
Functions 
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(x^3) or f(x) = (x+1)/(x1) for x ? 1 (x not equal to 1). 


912.F.BF.4a 
11 
Functions 
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(x^3) or f(x) = (x+1)/(x1) for x ? 1 (x not equal to 1). 


912.F.BF.4a 
12 
Functions 
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(x^3) or f(x) = (x+1)/(x1) for x ? 1 (x not equal to 1). 


912.F.BF.4b 
9 
Functions 
Verify by composition that one function is the inverse of another. 


912.F.BF.4b 
10 
Functions 
Verify by composition that one function is the inverse of another. 


912.F.BF.4b 
11 
Functions 
Verify by composition that one function is the inverse of another. 


912.F.BF.4b 
12 
Functions 
Verify by composition that one function is the inverse of another. 


912.F.BF.4c 
9 
Functions 
Read values of an inverse function from a graph or a table, given that the function has an inverse. 


912.F.BF.4c 
10 
Functions 
Read values of an inverse function from a graph or a table, given that the function has an inverse. 


912.F.BF.4c 
11 
Functions 
Read values of an inverse function from a graph or a table, given that the function has an inverse. 


912.F.BF.4c 
12 
Functions 
Read values of an inverse function from a graph or a table, given that the function has an inverse. 


912.F.BF.4d 
9 
Functions 
Produce an invertible function from a noninvertible function by restricting the domain. 


912.F.BF.4d 
10 
Functions 
Produce an invertible function from a noninvertible function by restricting the domain. 


912.F.BF.4d 
11 
Functions 
Produce an invertible function from a noninvertible function by restricting the domain. 


912.F.BF.4d 
12 
Functions 
Produce an invertible function from a noninvertible function by restricting the domain. 


912.F.BF.5 
9 
Functions 
Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. 


912.F.BF.5 
10 
Functions 
Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. 


912.F.BF.5 
11 
Functions 
Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. 


912.F.BF.5 
12 
Functions 
Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. 


912.F.LE.1 
9 
Functions 
Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions. 


912.F.LE.1 
10 
Functions 
Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions. 


912.F.LE.1 
11 
Functions 
Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions. 


912.F.LE.1 
12 
Functions 
Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions. 


912.F.LE.1a 
9 
Functions 
Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. 


912.F.LE.1a 
10 
Functions 
Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. 


912.F.LE.1a 
11 
Functions 
Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. 


912.F.LE.1a 
12 
Functions 
Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. 


912.F.LE.1b. 
9 
Functions 
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. 


912.F.LE.1b. 
10 
Functions 
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. 


912.F.LE.1b. 
11 
Functions 
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. 


912.F.LE.1b. 
12 
Functions 
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. 


912.F.LE.1c 
9 
Functions 
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 


912.F.LE.1c 
10 
Functions 
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 


912.F.LE.1c 
11 
Functions 
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 


912.F.LE.1c 
12 
Functions 
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 


912.F.LE.2 
9 
Functions 
Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). 


912.F.LE.2 
10 
Functions 
Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). 


912.F.LE.2 
11 
Functions 
Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). 


912.F.LE.2 
12 
Functions 
Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). 


912.F.LE.3 
9 
Functions 
Construct and compare linear, quadratic, and exponential models and solve problems. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 


912.F.LE.3 
10 
Functions 
Construct and compare linear, quadratic, and exponential models and solve problems. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 


912.F.LE.3 
11 
Functions 
Construct and compare linear, quadratic, and exponential models and solve problems. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 


912.F.LE.3 
12 
Functions 
Construct and compare linear, quadratic, and exponential models and solve problems. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 


912.F.LE.4 
9 
Functions 
Construct and compare linear, quadratic, and exponential models and solve problems. For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. 


912.F.LE.4 
10 
Functions 
Construct and compare linear, quadratic, and exponential models and solve problems. For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. 


912.F.LE.4 
11 
Functions 
Construct and compare linear, quadratic, and exponential models and solve problems. For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. 

