University of Texas at Austin
Mathematics Teks Toolkit: Making Connections
In this instructional activity, students will use input/output tables to explore functions, equations, and graphs.
Purple Math
Purplemath: General Polynomials
Confused about graphing or just need a refresher? This explanation focuses on graphing higher-power polynomials along with radical functions, rational functions, and piecewise functions. Plenty of examples are included.
Math Planet
Math Planet: Algebra 1: Representing Functions as Rules and Graphs
Provides examples and a video lesson that illustrates how to represent a function as a rule or graph.
Cool Math
Coolmath: Pre Calculus Graphs to Know and Love
A list and visuals of standard graphs from y = x to an absolute value.
Khan Academy
Khan Academy: Recognizing Functions From Graphs
In this exercise, students practice recognizing functions from graphs. Students receive immediate feedback and have the opportunity to watch a video, get hints, or try questions repeatedly.
Illustrative Mathematics
Illustrative Mathematics: F Le Exponential Kiss
The purpose of this task is to use technology to study the behavior of some exponential and logarithmic graphs and to manipulate some explicit logarithmic and exponential expressions. Aligns with HSF-LE.A.4, F-BF.B.5, and F-IF.C.7.e.
Illustrative Mathematics
Illustrative Mathematics: F Le Comparing Graphs of Functions
The goal of this task is to use appropriate tools to compare graphs of several functions. In addition, students are asked to study the structure of the different expressions to explain why these functions grow as they do. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: F if the Customers
This is a beginning lesson on the concept of functions. The context is a business that has a database of customer names and phone numbers in a table and students must decide if a function is involved. Aligns with F-IF.A.1 and 8.F.A.1.
Illustrative Mathematics
Illustrative Mathematics: F if Average Cost
In this task, young scholars must calculate the average cost for a DVD recording for different numbers of DVDs and explain why the cost levels off as the number of DVDs goes up. Aligns with F-IF.B.4 and F-IF.B.5.
Illustrative Mathematics
Illustrative Mathematics: F If.3 Snake on a Plane
In a video game called Snake, a player moves a snake through a square region in the plane, trying to eat the white pellets that appear. This task has students approach a function via both a recursive and an algebraic definition, in the...
Illustrative Mathematics
Illustrative Mathematics: F if Graphs of Power Functions
In this task, young scholars are asked to sketch and label the graphs of different (positive) powers of x. Aligns with F-IF.C.7.c.
Illustrative Mathematics
Illustrative Mathematics: F if.c Analyzing Graphs
For this task, students are presented with four different equations and asked to match them with their graphs, then respond to questions about the characteristics of the constants. Aligns with F-IF.C.
Illustrative Mathematics
Illustrative Mathematics: F if Your Father
This is a simple task which has students analyze functions where they assign a father to each student. It addresses the idea that not all functions have real numbers as domain and range values, and the issue of when a function admits an...
Illustrative Mathematics
Illustrative Mathematics: F if the Parking Lot
In this task about parking lot rates, students investigate what a function is and explain their reasoning. Aligns with F-IF.A.1.
Illustrative Mathematics
Illustrative Mathematics: F if Telling a Story With Graphs
For this task, students are presented with three weather-related graphs - on temperature, solar radiation, and precipitation. They are asked to describe the function represented in each graph and tell a more detailed story using...
Illustrative Mathematics
Illustrative Mathematics: F if How Is the Weather?
For this task, learners are presented with three graphs that show solar radiation as a function of time. They are asked to match each graph to the corresponding description of the weather during the day. Aligns with F-IF.B.4.
Illustrative Mathematics
Illustrative Mathematics: F if Interpreting the Graph
In this task, learners are asked to label points on the graph of a function that illustrate several statements. Aligns with F-IF.A.
Illustrative Mathematics
Illustrative Mathematics: F if Identifying Graphs of Functions
For this task, learners are presented with four function equations and four graphs of functions showing -2 less than or equal to x, which is less than or equal to +2. They are asked to match each function to the corresponding graph and...
Illustrative Mathematics
Illustrative Mathematics: F if Warming and Cooling
Students are presented with a graph showing temperature over a period of 20 hours and are asked to read and interpret the graph. Aligns with F-IF.B.4.
Illustrative Mathematics
Illustrative Mathematics: F if Influenza Epidemic
Students are presented with a graph showing the spread of an influenza epidemic through a city. They are asked to read and interpret the graph and the equation for its function. Aligns with F-IF.B.4.
Illustrative Mathematics
Illustrative Mathematics: F Bf 1,000 Is Half of 2,000
This task is about an online mathematics organization that is trying, over a four-year period, to generate 2,000 math problems that cover all grades. This real-life modeling task could serve as a summative exercise that draws on many...
Illustrative Mathematics
Illustrative Mathematics: F if Model Airplane Acrobatics
In this task, a model airplane pilot is practicing flying her airplane in a big loop for an upcoming competition. The task could serve as an introduction to periodic functions and as a lead-in to sinusoidal functions. By visualizing the...
Illustrative Mathematics
Illustrative Mathematics: F Bf.3 Transforming the Graph of a Function
This task examines, in a graphical setting, the impact of adding a scalar, multiplying by a scalar, and making a linear substitution of variables on the graph of a function f. There is no formula for the function so the focus is on...