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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 912
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.
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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.
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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.
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The Function Challenge
 Bill Graham

Algebra, difficulty level 2. Arrange a series of functions in the order that will produce the largest output.
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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.
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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.
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Sierpinski Stages
 Steve Risberg

Algebra, difficulty level 2. Find and use patterns to determine the total perimeter of an interesting shape.
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The Straggler Shakes Hands
 Melissa Kennedy, Susan Rose, Ethel Breuche

Algebra, difficulty level 3. There were one hundred fortyone handshakes in all. How many people did the straggler know? This puzzle involves a quadratic expression and triangular numbers.
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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.
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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.
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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?
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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?
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