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Chapter 1: Problem 152

Assume that \((a, b)\) is a point on the graph of \(f .\) What is the corresponding point on the graph of each of the following functions? $$y=f(x)-3$$

Short Answer

Expert verified
The point corresponding to \((a, b)\) on the graph of \(y = f(x) - 3\) is \((a, b - 3)\).

Step by step solution

01

Understand the given point

A point on a graph of a function is generally given in the form \((a, b)\) where \(a\) is the value on the x-axis (input) and \(b\) is the value on the y-axis (output of the function for the input \(a\)). Here, we are given a point on the graph of the function \(f\), which is \((a,b)\). This means that when the function \(f\) is evaluated at \(a\), the output value is \(b\).
02

Understand the transformation

The function \(f(x) - 3\) represents a vertical shift of \(f(x)\) downwards by 3 units. This means that for every point on the graph of the function \(f\), it's image on the graph of \(f(x) - 3\) is a point that is 3 units lower.
03

Apply the transformation to the given point

So, the corresponding point on the graph of \(f(x) - 3\) to the point \((a,b)\) on the graph of \(f\) would be \((a, b - 3)\) since it would be 3 units lower than \((a,b)\). This is because the original output \(b\) is decreased by 3 units to become \(b - 3\)

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