# Interpret Features of a Function

Videos and lessons to help High School students understand how a function 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.
• Distinguish linear, quadratic, and exponential relationships based on equations, tables, and verbal descriptions.
• Given a function in a table or in algebraic or graphical form, identify key features such as x- and y-intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior.
• Use key features of an algebraic function to graph the function.

Common Core: HSF-IF.B.4

F.IF.4 - Interpret Key Features of the Graph of a Function
The function f(t) = -5t2 + 20t + 60 models the approximate height of an object t seconds after it is launched.
a) What is its maximum height?
b) How many seconds does it take to reach its maximum height?
c) How many seconds does it take for the object to return to the ground after the launch?

Interpreting intercepts of linear functions
After several days of camping and long distance bicycle riding, you decide to ride straight home at a constant rate. After 2 hours of riding, you are 10 km from home and after 4 hours of riding, you are 5 km from home. Once you begin to ride home, in how many hours would you finish your bike ride and arrice at home?
x and y intercepts of exponential functions
How to find the x and y intercepts of an exponential function from a graph, equation, and word description.

End Behavior of Linear and Exponential Functions
How to find end behaviors of linear and exponential functions from graphs, tables, and equations.
Interpreting Linear Functions (Part 1)
Interpreting graphs of linear functions, including horizontal and vertical asymptotes, and rate of change.

Interpreting Linear Functions (Part 2)
Interpreting graphs of linear functions, including horizontal and vertical asymptotes, and rate of change.
Interpreting features of functions (Example 1).

Interpreting features of functions (Example 2).
Interpreting Graphs of Exponential Functions
In this video one is supplied with a real world situation and a graph corresponding to that situation. The graph is then used to answer a series of questions.

Recognizing features of functions (Example 1).

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.