Graphing Square-Root Functions
Graph square-root functions in Grade 9 Algebra by building a table of values and plotting key points. Identify domain restrictions and the starting point of each curve.
Key Concepts
New Concept A square root function is a function that contains a square root of a variable. What’s next Next, you’ll master graphing these functions by learning how to shift and reflect the basic parent function, $y = \sqrt{x}$.
Common Questions
How do you graph a square-root function using a table?
Choose x-values that are perfect squares or make the expression under the radical non-negative. Compute y = √x for each, plot the ordered pairs, and connect them with a smooth curve starting from the leftmost valid point.
What is the domain of a square-root function?
The domain is all x-values that make the expression under the radical greater than or equal to zero. For f(x) = √(x - h), set x - h ≥ 0 and solve to get x ≥ h, so the domain starts at the vertex x-coordinate.
Where does the graph of a square-root function start?
The graph begins at the starting point (also called the endpoint or vertex), determined by setting the radicand equal to zero. To the left of this point the function is undefined in the real numbers, and the curve extends to the right.