Problem 150 - Precalculus Essentials

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? $$y=2 f(x)$$

Step-by-Step Solution

Answer

The corresponding point on the graph of the function \(y = 2f(x)\) would be \((a, 2b)\).

Step 1: Understanding the Function \(y=2f(x)\)

The function \(y = 2f(x)\) essentially doubles the y-coordinate of any point on the graph \(f\). So if we know a point \((a, b)\) on the graph of \(f\), the corresponding point on the graph of \(y = 2f(x)\) would have the same x-coordinate (\(a\)) and the y-coordinate would be double, which is \(2b\).

Step 2: Finding the corresponding point

Given the point \((a, b)\) on \(f\), the corresponding point on the graph of \(y = 2f(x)\) is \((a, 2b)\).