Square Root Function
The square root function is defined by a square root expression and is a key parent function in Grade 11 enVision Algebra 1 (Chapter 10: Working With Functions). To evaluate f(x) = √x, substitute the given x-value into the expression under the radical and simplify. The domain of the basic square root function is x ≥ 0, since square roots of negative numbers are not real. Mastering evaluation of square root functions prepares students for graphing, domain analysis, and transformations of radical functions.
Key Concepts
Property A square root function is a function that is defined by a square root expression. To evaluate a square root function, we find the value of $f(x)$ for a given value of $x$ by substituting the value and simplifying the square root.
Examples For the function $f(x) = \sqrt{2x 1}$, to find $f(5)$, substitute 5 for $x$: $f(5) = \sqrt{2(5) 1} = \sqrt{9} = 3$. For the function $g(x) = \sqrt{x + 7}$, to find $g(2)$, substitute 2 for $x$: $g(2) = \sqrt{2 + 7} = \sqrt{9} = 3$. For the function $h(x) = \sqrt{3x + 6}$, to find $h( 3)$, substitute 3 for $x$: $h( 3) = \sqrt{3( 3) + 6} = \sqrt{ 3} = \sqrt{3}$.
Explanation A square root function is a function that contains a square root symbol with the variable inside the radical. To evaluate it, you substitute the given number for the variable $x$ and then simplify the expression under the square root symbol.
Common Questions
What is a square root function?
A square root function is a function defined by a square root expression, such as f(x) = √x, where the variable appears under the radical sign.
How do you evaluate a square root function at a given x-value?
Substitute the x-value into the expression under the square root and simplify: for f(x) = √x, f(25) = √25 = 5.
What is the domain of f(x) = √x?
The domain is x ≥ 0, since you cannot take the square root of a negative number and get a real result.
What is the range of f(x) = √x?
The range is f(x) ≥ 0, since square roots always yield non-negative outputs.
What happens to the domain when the square root function is translated?
The domain shifts with horizontal translations. For f(x) = √(x − 3), the domain becomes x ≥ 3.
How does a square root function differ from a quadratic function?
A square root function is the inverse of a quadratic function (on a restricted domain). Its graph is a half-curve starting at a point, not a full parabola.