Question

horizontal shifts quick check
use the image to answer the question.
which of the following identifies the value of k that would correctly characterize the horizontal shift shown in the graph if the line to the left represents ( y = f(x) ) and the line to the right represents ( y = f(x - k) )?
(1 point)
5
8
10
2

Explanation:

Step1: Analyze the horizontal shift formula

For a function \(y = f(x)\) shifted to \(y = f(x - k)\), the shift is \(k\) units to the right.

Step2: Calculate the shift using points

Take a point on \(y = f(x)\) say \((5,45)\) and on \(y = f(x - k)\) the corresponding point is \((10,45)\).
The difference in \(x -\)coordinates: \(10-5=5\).

Answer:

5