Problem 150

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

Verified
Answer
The corresponding point on the graph of y=2f(x) would be (a, 2b).
1Step 1: Identify the Transformation
First, identify what type of transformation is occurring. In the function y=2f(x), the number 2 is multiplying the output of function f(x), and this results in a vertical stretching of the graph. The y-values of the function are doubled while x-values are unaffected.
2Step 2: Apply the Transformation
Apply the transformation to the given point (a, b). Since we know that the x-values stay the same and the y-values are doubled, the corresponding point on the graph of y=2f(x) for any point (a, b) on the original graph would be (a, 2b).