Choose the function that is a “parent function”.
ƒ( x) = x + 3
ƒ( x) = | x - 3|
ƒ( x) = ( x - 3) 2
ƒ( x) = √x
The parent function among the given options is ƒ(x) = x.
A "parent function" refers to a basic function from which other functions can be derived through transformations. To identify the parent function among the given options, we need to find the function that hasn't been subject to any transformations.
Let's analyze the given functions:
1. ƒ(x) = x + 3
This function involves adding 3 to the input value x. This represents a vertical shift upwards by 3 units. It is not the parent function since it has a transformation.
2. ƒ(x) = |x - 3|
This function involves taking the absolute value of x - 3. This represents a reflection of the part of the graph below the x-axis. It is not the parent function since it has a transformation.
3. ƒ(x) = (x - 3)^2
This function involves squaring the quantity (x - 3). This represents a vertical compression/stretch and a horizontal shift to the right by 3 units. It is not the parent function as it has transformations.
4. ƒ(x) = √x
This function represents the square root of x, without any additional transformations. It is the parent function of all square root functions.
Therefore, the function ƒ(x) = √x is the parent function among the given options.