Meaning before procedure
The parent square-root function f(x) = √x begins at (0,0), exists only for x ≥ 0, and increases while flattening. Perfect-square x-values create exact anchor points.
- Parent function
- The simplest function in a transformation family.
- Endpoint
- The starting point (0,0) of y = √x.
- Domain
- All allowed x-values: x ≥ 0.
- Range
- All output values: y ≥ 0.
Interactive visual model
Adjust a, h, and k and compare the transformed curve with the square-root parent.
Change one control at a time and describe what changes—and what stays invariant.
A dependable four-step method
- Choose perfect-square x-values.
- Compute their principal square roots.
- Plot the endpoint and anchor points.
- Connect with an increasing, flattening curve only in the domain.
Watch the reasoning, not just the answer
Example 1: Find three points on y = √x.
Example 2: Determine whether (9,3) lies on y = √x.
Example 3: State the domain and range.
Predict, decide, check, and revise
Build a valid reasoning path
Choose the decisions in the order a careful solver would use them for this concept.
The reasoning path changes as each decision is selected.
Check the foundation
On y = √x, what y-value corresponds to x = 0?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
On y = √x, what y-value corresponds to x = 1?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Apply the method with support
On y = √x, what y-value corresponds to x = 4?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
On y = √x, what y-value corresponds to x = 9?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
On y = √x, what y-value corresponds to x = 16?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Work without step prompts
On y = √x, what y-value corresponds to x = 25?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
On y = √x, what y-value corresponds to x = 36?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
On y = √x, what y-value corresponds to x = 49?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
On y = √x, what y-value corresponds to x = 64?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Demonstrate durable understanding
On y = √x, what y-value corresponds to x = 81?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
On y = √x, what y-value corresponds to x = 100?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
On y = √x, what y-value corresponds to x = 121?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
On y = √x, what y-value corresponds to x = 144?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
On y = √x, what y-value corresponds to x = 169?
Your prediction is locked so the record preserves what you thought before recognition choices appeared.
Explain, compare, and revise
Explain how a table of perfect squares predicts the shape and direction of y = √x.
Guided self-check
Judge the locked first attempt against every criterion.
Model reasoning
Using x = 0, 1, 4, 9, 16 gives y = 0, 1, 2, 3, 4. Increasing y by 1 requires increasingly larger changes in x, so the graph rises but gradually flattens to the right.
The learner record reveals exact answers and model reasoning only after an attempt.