# Common Core Mathematics 9-12 |

**Cluster** | Analyze functions using different representations |

| ** Grade 9-12** |

| F.IF.7. | Graph functions expressed symbolically and show key features of
the graph, by hand in simple cases and using technology for more
complicated cases. |

| F.IF.7.a. | Graph linear and quadratic functions and show intercepts,maxima, and minima. |

| F.IF.7.b. | Graph square root, cube root, and piecewise-defined functions,
including step functions and absolute value functions. |

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

| F.IF.7.d. | (+) Graph rational functions, identifying zeros and asymptotes
when suitable factorizations are available, and showing end
behavior. |

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

| F.IF.8. | Write a function defined by an expression in different but equivalent
forms to reveal and explain different properties of the function. |

| F.IF.8.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.IF.8.b. | 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 or decay. |

| F.IF.9. | 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.* |