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Chapter 2: Problem 130

What must be done to a function's equation so that its graph is shifted horizontally to the right?

Short Answer

Expert verified
To shift a function's graph horizontally to the right, you need to subtract a positive constant from the input variable in the function equation. The new equation will be \(y = f(x - k)\), where \(k\) is the number of units you want to shift the graph to the right.

Step by step solution

01

Understanding Function Transformations

Function transformations are changes to the original characteristics of a function that yield a new function. For a function \(y = f(x)\), horizontal shifts occur when changes are made to the input variable, \(x\).
02

Determining Direction of Shift

Modification to the input is based on the direction of shift we want to achieve. As the problem asks for a shift to the right, we subtract a positive constant, \(k\), from the input variable.
03

Writing New Function for Right-shifted Graph

To shift the graph of a function to the right by \(k\) units, the original function equation, \(y = f(x)\), is transformed into \(y = f(x - k)\). This new function's graph will be the same as the original but shifted \(k\) units to the right.

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