Question

If the function S(x) = sqrt4x + 1 is horizontally stretched by a factor of 2, reflected across the

x-axis, and translated up 3 units, write the equation of the new function,
It’s number 15

Answer 1

The new function after horizontal stretching by a factor of 2, reflecting across the x-axis, and translating up 3 units is S(x) = -√(2x) + 4.

Step-by-step explanation:

The given function is S(x) = √(4x) + 1. When this function undergoes a horizontal stretch by a factor of 2, it becomes S(x) = √(4(x/2)) + 1 = √(2x) + 1. Then, reflecting it across the x-axis changes its sign, and the function becomes S(x) = -√(2x) + 1. Finally, translating the function up by 3 units, we obtain the new function:

S(x) = -√(2x) + 1 + 3 = -√(2x) + 4