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Chapter 1: Problem 10

Fill in the blank: The constant function and the identity function are two special types of _____ functions.

Short Answer

Expert verified
The constant function and the identity function are two special types of linear functions.

Step by step solution

01

Identify the nature of a constant function

A constant function is a function whose output value is the same for any input value. In mathematical terms, if we denote the function as \(f(x)\), it can be defined as \(f(x) = c\), where \(c\) is a constant.
02

Identify the nature of an identity function

An identity function is where the output value is same as the input value. In mathematical terms, if we denote the function as \(f(x)\), it can be defined as \(f(x) = x\).
03

Determine the type of functions

From the properties shared by constant and identity functions, it is evident that both fall under the category of linear functions because both can be graphed as a straight line on a 2D Cartesian Co-ordinate system.

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