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Constant Function

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Constant Function

Study Guide

Key Definition

A constant function is a linear function for which the range does not change no matter which member of the domain is used. In mathematical terms, $f ( x_1 ) = f ( x_2 )$ for any $x_1$ and $x_2$ in the domain. With a constant function, for any two points in the interval, a change in x results in a zero change in $f ( x )$. The graph of a constant function is always a horizontal line.

Important Notes

In a constant function, the range does not change regardless of the domain.
In simple terms, no matter what x-value you plug into the function, the output will always be the same.

Mathematical Notation

$f ( x_1 ) = f ( x_2 )$ means that for any two values in the domain, the function will return the same output.

$f ( x )$ is the notation used to represent a function.

Remember to use proper notation when solving problems

Why It Works

A constant function works because it is a specific type of linear function where the slope is zero. This means that no matter what x-value you choose, the y-value will always be the same, making the graph of the function a horizontal line.

Remember

In a constant function, any change in x results in zero change in $f ( x )$.

Quick Reference

Function Notation:$f ( x )$

Constant Function Property:$f ( x_1 ) = f ( x_2 )$

Understanding Constant Function

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A constant function is a type of linear function where the slope is zero. This means that no matter what x-value you choose, the f(x) or y-value will always be the same. Hence, the graph of a constant function is a straight horizontal line.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following is a constant function?

Real-World Problem

Question Exercise

Intermediate

Temperature Scenario

Imagine you are observing the temperature inside your classroom over a period of time. You note that the temperature remains constant at 22 degrees Celsius. This is an example of a constant function in real life.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If a function $f(x)$ is such that for any two points $x_1$ and $x_2$ in the domain, $f(x_1) = f(x_2)$. What type of function is this?

Challenge Quiz

Single Choice Quiz

Advanced

What will be the graph of a constant function $f(x) = k$?

Recap

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Review key concepts and takeaways