Compare Two Functions
Videos and lessons with examples and solutions to help High School students learn how to compare properties of two functions each represented in different ways (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.
Compare intercepts, maxima and minima, rates of change, and end behavior of two quadratic functions, where one is represented algebraically, graphically, numerically in tables, or by verbal descriptions, and the other is modeled using a different representation.
Comparing features of different functions example 1
Example:
Which function has no x-intercept?
Comparing features of different functions example 2
Example:
Which quadratic has the lowest maximum value?
Comparing features of different functions example 3
Example:
Which of the features are shared by f(x) and g(x)?
Answer:
• They are both odd.
• They share an x-intercept.
• They have the same end behavior.
• They have a relative maximum at the same x value.
Comparing features of functions
Example:
x is a linear function whose table of values are shown below.
Which graph shows functions that are increasing faster than f?
Comparing features of functions
Example:
Charles and Tammy lives the same distance from work, and they started walking to work at the same time. They both walked at constant speeds, though not necessarily at the same speed. Charles' distance from work is shown in the following table.
Which of these sentence could possibly be true?
• Tammy started 830m from work, and walked towards work at 2 meters per second.
• Tammy started 900m from work, and walked towards work at 7/5 meters per second.
• Tammy started 900m from work, and walked towards work at 5/7 meters per second.
• Tammy started 760m from work, and walked towards work at 7/5 meters per second.
• Tammy started 830m from work, and walked towards work at 1.4 meters per second.
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