Question

If you horizontally stretch the square root function, f(x)=√x, by 1/4 of a unit, what is the equation of the new function?

Option a: f(x) = √(x + 1/4)
Option b: f(x) = √(4x)
Option c: f(x) = √(x - 1/4)
Option d: f(x) = √(x) + 1/4

Answer 1

To horizontally stretch the square root function f(x)=√x by 1/4 of a unit, you multiply the input variable by the reciprocal of the stretch factor, which is 4. Therefore, the new function's equation is f(x) = √(4x), which corresponds to Option b.

Step-by-step explanation:

If you horizontally stretch the square root function f(x)=√x by 1/4 of a unit, the operation that corresponds to a horizontal stretch is to multiply the input variable by the reciprocal of the stretch factor. In this case, since we are stretching it by 1/4, the reciprocal is 4. Hence, you multiply the input variable x by 4. The equation of the new function will be f(x) = √(4x), which is Option b.