The transformation of the graph of the parent function results in the graph of f(x) = 10·√x + 3, are;
- A vertical stretch of 10 units
- A vertical translation of 3 units upwards
Please find attached the graphs of the parent square root function and f(x) = 10·√x + 3, created with MS Excel, showing the vertical stretch and upwards translation of the parent function
The transformation of the graph of the parent function by the function f(x) are found as follows;
The transformation of the parent square root function represented by the graph of f(x) = 10·√x + 3
The transformation rules indicates that the transformation of a function by the product of the parent function and a constant results in a vertical stretch when the absolute value of the constant is larger than 1, and it results in a vertical compression when the absolute value of the constant is less than 1, therefore, where the constant is 10, we get;
The parent function is stretched vertically by a factor of 10
(x, y) → a·f(x) → (x, a·y)
Therefore, the coordinates of the corresponding x- and y-values of the function f(x) = 10·√x, are therefore, (x, 10·y)
The coordinates of the y-values of the function f(x) following a transformation f(x) + x is a translation x units upwards
Therefore, the coordinates of the function f(x) following a transformation, f(x) + 3, is a translation 3 units upwards
Therefore, the coordinates of the x- and y-values of the function f(x) following the transformation of the parent square root function are therefore;
Transformation f(x) = 10·√x + 3
(x, y) ⇒ 10·√x + 3 ⇒ (x, 10·√x + 3)
Please find attached the graph of the parent function, y = √x, and the function, y = 10·√x + 3, plotted on the same coordinate plane created with MS Excel