Answer:
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