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Chapter 2: 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 corresponding point on the graph of the function \(y = f(x) - 3\) is \((a, b-3) \).

Step by step solution

01

Identify the given point

We are given a point \((a, b)\) on the graph of the function \(f(x)\). This means that \(f(a)=b\).
02

Apply the Transformation

For the function \(y=f(x)-3\), all y-values are subtracted by 3, so every point \((x, y)\) on the original graph corresponds to \((x, y-3)\) on the new graph.
03

Determine the corresponding point

So, the point \((a, b)\) on the original function \(f(x)\) corresponds to \((a, b-3)\) on the new function \(y = f(x) - 3\).

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