Overview

Algebra 2

24. MA.912.AR.7.3

24.1 Square root of a function

The Square Root Function

y = the square root of x starts at the origin and is only defined for x greater than or equal to 0.

What You'll Learn

y = the square root of x is defined only for x greater than or equal to 0.

The domain is x greater than or equal to 0; the range is y greater than or equal to 0.

Key points: square root of 0 is 0, of 1 is 1, of 4 is 2, of 9 is 3.

The curve flattens as x grows, since y only doubles when x quadruples.

Squaring both sides gives y squared = x, the upper half of a sideways parabola.

What You'll Practice

Graphing square root transformations of linear functions using tables of values

Sketching square root curves from piecewise function graphs

Identifying domain and range for square root of functions

Locating invariant points on transformed graphs

Why This Matters

Understanding square root transformations is essential for analyzing more complex functions in algebra and calculus. You'll use these graphing techniques when working with radical equations, modeling real-world scenarios involving rates of change, and preparing for function composition in higher-level math.

This Unit Includes

4 Video lessons

Practice exercises

Learning resources

Skills

Square Root Functions

Function Transformations

Graphing

Domain and Range

Invariant Points

Concavity

FL Curriculum Aligned