F-IF. Interpreting Functions

F-IF.A. Understand the concept of a function and use function notation.

• Interpreting the graph

F-IF.A.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 $y = f(x)$.

• Domains
• Do two points always determine a linear function?
• Finding the domain
• Parabolas and Inverse Functions
• Points on a graph
• The Customers
• The Parking Lot
• Using Function Notation I
• Your Father

F-IF.A.2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

• Cell phones
• Random Walk II
• The Random Walk
• Using Function Notation II
• Yam in the Oven

F-IF.A.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 $n \ge 1$.

• Snake on a Plane

F-IF.B. Interpret functions that arise in applications in terms of the context.

• Pizza Place Promotion

F-IF.B.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.

• As the Wheel Turns
• Average Cost
• Containers
• F-IF From the flight deck
• F-IF Graphing Stories
• Hoisting the Flag 1
• Hoisting the Flag 2
• How is the Weather?
• Influenza epidemic
• Lake Sonoma
• Logistic Growth Model, Abstract Version
• Logistic Growth Model, Explicit Version
• Model air plane acrobatics
• Modeling London's Population
• Playing Catch
• Solar Radiation Model
• Telling a Story With Graphs
• The Aquarium
• The Canoe Trip, Variation 1
• The Canoe Trip, Variation 2
• The story of a flight
• Throwing Baseballs
• Warming and Cooling
• Words - Tables - Graphs

F-IF.B.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.

• Average Cost
• Oakland Coliseum
• The Canoe Trip, Variation 1
• The Canoe Trip, Variation 2
• The restaurant

F-IF.B.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.

• 1,000 is half of 2,000
• Laptop Battery Charge 2
• Mathemafish Population
• Temperature Change
• The High School Gym

F-IF.C. Analyze functions using different representations.

• Analyzing Graphs

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

• Graphs of Quadratic Functions
• Identifying graphs of functions
• Modeling London's Population

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

• Graphs of Quadratic Functions

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

• Bank Account Balance

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

• Graphs of Power Functions
• Running Time

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

• Graphing Rational Functions

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

• Exponential Kiss
• Identifying Exponential Functions

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

• Which Function?

F-IF.C.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.

• Springboard Dive
• Which Function?

F-IF.C.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.

• Carbon 14 dating in practice I

F-IF.C.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.

• Throwing Baseballs