Problem 152
Question
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? $$y=f(x)-3$$
Step-by-Step Solution
Verified Answer
The corresponding point on the graph of the function \(y = f(x) - 3\) is \((a, b-3) \).
1Step 1: Identify the given point
We are given a point \((a, b)\) on the graph of the function \(f(x)\). This means that \(f(a)=b\).
2Step 2: 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.
3Step 3: 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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