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use of variables
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Functions and Relations
Solving these problems is more easily done if the student can find a function or rule to fit data which is given or collected. Problems may also focus on function notation and ideas such as domain and range.

Related Resources
Interactive resources from our Math Tools project:
   Algebra: Functions & Relations
The closest match in our Ask Dr. Math archives:
   High School: Functions
NCTM Standards:
   Algebra Standard for Grades 9-12

Access to these problems requires a Membership.

The Chip Swap Game - Ethel Breuche
Algebra, difficulty level 4. The object of this game is to swap the positions of the different colored chips. Count the number of moves and, as you increase the number of chips, find the general formula. ... more>>

Filling Glasses - Annie Fetter
Algebra, difficulty level 2. Match up each of the three glasses with the graph that best describes the height of the water in the glass over time, when the glass is filled with water at a constant rate. ... more>>

From Here to There - Steve Risberg
Algebra, difficulty level 2. Given descriptions of the rate schedules of a bus, a taxi, and a shuttle, choose the graphs that best illustrate the cost of riding each one. ... more>>

The Function Challenge - Bill Graham
Algebra, difficulty level 2. Arrange a series of functions in the order that will produce the largest output. ... more>>

Hiking Mount Hood - PoW staff
Algebra, difficulty level 1. Don hikes up and down a mountain at various speeds. Choose the graph that best represents his trip. ... more>>

Pizza Puzzle - Steve Risberg
Algebra, difficulty level 1. Given two pricing examples, determine a general equation for the cost of a Giordano's Giant gourmet pizza. ... more>>

Sierpinski Stages - Steve Risberg
Algebra, difficulty level 2. Find and use patterns to determine the total perimeter of an interesting shape. ... more>>

The Straggler Shakes Hands - Melissa Kennedy, Susan Rose, Ethel Breuche
Algebra, difficulty level 3. There were one hundred forty-one handshakes in all. How many people did the straggler know? This puzzle involves a quadratic expression and triangular numbers. ... more>>

Teeter Trio - Steve Risberg
Algebra, difficulty level 1. Find a function that expresses where a child sits on a seesaw in terms of her weight. ... more>>

To B or Not To B - Steve Risberg
Algebra, difficulty level 2. Given a letter pattern, find expressions for the number of B's and the ratio of B's to total letters in the nth term. ... more>>

Voter Turnout - Steve Risberg
Algebra, difficulty level 2. A group of students collected data on voter turnout for the recent election and plotted graphs broken down by age groups. Can you match each age group with its graph? ... more>>

The World's Meanest Math Teacher - Bill Graham
Algebra, difficulty level 3. Students seated around a circular table are being systematically eliminated. What's the rule to follow to be the last one eliminated? ... more>>

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