MA2015 (9-12) Algebra | 7. Interpret expressions that represent a quantity in terms of its context.* [A-SSE1] a. Interpret parts of an expression such as terms, factors, and coefficients. [A-SSE1a] b. Interpret complicated expressions by viewing one or more of their parts as a single entity. [A-SSE1b] Example: Interpret *P*(1+*r*)^{n} as the product of *P* and a factor not depending on *P*. |

MA2015 (9-12) Algebra | 9. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* [A-SSE3] a. Factor a quadratic expression to reveal the zeros of the function it defines. [A-SSE3a] b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. [A-SSE3b] c. Determine a quadratic equation when given its graph or roots. (Alabama) d. Use the properties of exponents to transform expressions for exponential functions. [A-SSE3c] Example: The expression 1.15^{t} can be rewritten as (1.15^{1/12})^{12t} ≈ 1.012^{12t} to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. |

MA2015 (9-12) Algebra | 28. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. *Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.** [F-IF4] |

MA2015 (9-12) Algebra | 31. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [F-IF7] a. Graph linear and quadratic functions, and show intercepts, maxima, and minima. [F-IF7a] b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. [F-IF7b] |

MA2015 (9-12) Algebra | 32. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F-IF8] a. 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. [F-IF8a] b. Use the properties of exponents to interpret expressions for exponential functions. [F-IF8b] Example: Identify percent rate of change in functions such as *y* = (1.02)^{t}, *y* = (0.97)^{t}, *y* = (1.01)^{12t}, and *y* = (1.2)^{t/10}, and classify them as representing exponential growth and decay. |

MA2015 (9-12) Algebra | 34. Write a function that describes a relationship between two quantities.* [F-BF1] a. Determine an explicit expression, a recursive process, or steps for calculation from a context. [F-BF1a] b. Combine standard function types using arithmetic operations. [F-BF1b] 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. |

MA2015 (9-12) Algebra | 36. 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 (9-12) Algebra | 37. Distinguish between situations that can be modeled with linear functions and with exponential functions. [F-LE1] a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. [F-LE1a] b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. [F-LE1b] c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. [F-LE1c] |

MA2015 (9-12) Algebra | 38. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). [F-LE2] |

MA2015 (9-12) Algebra | 39. Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [F-LE3] |

MA2015 (9-12) Algebraic Connections | 3. Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) Example: Solve problems involving compound interest, bacterial growth, carbon-14 dating, and depreciation. |

MA2015 (9-12) Algebra II | 30. Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [F-IF7] a. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. [F-IF7b] Example *f*(*x*) = 2*x*^{3} or *f*(*x*) = (*x*+1)/(*x*-1) for *x* ≠ 1. b. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. [F-IF7c] c. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. [F-IF7e] |

MA2015 (9-12) Algebra II | 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 (9-12) Algebra II with Trigonometry | 12. Interpret expressions that represent a quantity in terms of its context.* [A-SSE1] a. Interpret parts of an expression such as terms, factors, and coefficients. [A-SSE1a] b. Interpret complicated expressions by viewing one or more of their parts as a single entity. [A-SSE1b] Example: Interpret *P*(1+*r*)^{n} as the product of *P* and a factor not depending on *P*. |

MA2015 (9-12) Algebra II with Trigonometry | 21. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2] |

MA2015 (9-12) Precalculus | 16. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. (*Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Determine odd, even, neither.*)* [F-IF4] (Alabama) |

MA2015 (9-12) Algebra II with Trigonometry | 30. Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [F-IF7] a. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. [F-IF7b] b. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. [F-IF7c] c. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. [F-IF7e] |

MA2015 (9-12) Algebra II with Trigonometry | 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 (9-12) Precalculus | 25. Compare effects of parameter changes on graphs of transcendental functions. (Alabama) Example: Explain the relationship of the graph *y* = *e*^{x-2} to the graph *y* = *e*^{x}. |