Topic: Interpreting Functions |
Common Core Mathematics 9-12 |
| Cluster Understand the concept of a function and use function notation |
| | Grade 9-12 |
| | | F.IF.1. | Understand that a function from one set (called the domain) to
another set (called the range) assigns to each element of the domain
exactly one element of the range. If f is a function and x is an element
of its domain, then f(x) denotes the output of f corresponding to the
input x. The graph of f is the graph of the equation y = f(x). |
| | | F.IF.2. | Use function notation, evaluate functions for inputs in their domains,
and interpret statements that use function notation in terms of a
context. |
| | | F.IF.3. | Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, the
Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) +
f(n-1) for n ≥ 1. |
| Cluster Interpret functions that arise in applications in terms of the context |
| | Grade 9-12 |
| | | F.IF.4. | 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.IF.5. | Relate the domain of a function to its graph and, where applicable, to
the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. |
| | | F.IF.6. | Calculate and interpret the average rate of change of a function
(presented symbolically or as a table) over a specified interval.
Estimate the rate of change from a graph. |
| 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. |