Question

Transformation of a square root function
f(x)a√b(x-c) +d

Answer 1

A square root function can be transformed by adjusting the values of a, b, c, and d. This affects the vertical and horizontal stretch/compression, as well as the horizontal and vertical shift of the function.

Step-by-step explanation:

A square root function can be transformed by adjusting the values of a, b, c, and d. Let's break it down:

1. a: This determines the vertical stretch or compression of the function. If a is positive, the function is stretched vertically, and if a is negative, it is compressed vertically.
2. b: This determines the horizontal stretch or compression. If b is greater than 1, the function is compressed horizontally, and if b is between 0 and 1, it is stretched horizontally.
3. c: This determines the horizontal shift of the function. If c is positive, the function is shifted to the right, and if c is negative, it is shifted to the left.
4. d: This determines the vertical shift of the function. If d is positive, the function is shifted upward, and if d is negative, it is shifted downward.

By adjusting these values, you can transform the square root function.