How is the graph of y = square root of - 2x related to its parent function y = square root x

Step-by-step explanation:

The parent function is the simplest form of the type of function given.

y = √ x

For a better explanation, assume that

y = √ x is f (x) = √ x and y = √ x is g (x) = √ x. f (x) = √ x g (x) = √ x

The transformation from the first equation to the second one can be found by finding

a, h, and k for each equation. y = a √ x - h + k Factor a 1 out of the absolute value to make the coefficient of x equal to 1. y = √ x Find a, h, and k for y = √ x. a = 1 h = 0 k = 0

The horizontal shift depends on the value of h. When h > 0, the horizontal shift is described as: g (x) = f (x + h) - The graph is shifted to the left h units.

g (x) = f (x - h) - The graph is shifted to the right h units.

Horizontal Shift: None

The vertical shift depends on the value of k. When k > 0, the vertical shift is described as: g (x) = f (x) + k - The graph is shifted up k units. g (x) = f (x) - k - The graph is shifted down k units.

Vertical Shift: None

The sign of a

describes the reflection across the x-axis. - a means the graph is reflected across the x-axis.

Reflection about the x-axis: None

The value of a describes the vertical stretch or compression of the graph. a > 1 is a vertical stretch (makes it narrower) 0 < a < 1 is a vertical compression (makes it wider)

Vertical Compression or Stretch: None

To find the transformation, compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis, and if there is a vertical stretch.

Parent Function: y = √ x

Horizontal Shift: None

Vertical Shift: None

Reflection about the x-axis: None

Vertical Compression or Stretch: None