Exploring Root Functions and Transformations Flashcard

Front

What transformation occurs when \( k \) is added to the square root function \( y = \sqrt{x} \)?

Back

Vertical shift.

Front

What is the domain of the function \( y = \sqrt[3]{x} \)?

Back

\((-\infty, \infty)\)

Front

Which of the following is a key feature of the cube root function?

Back

It is symmetric about the origin.

Front

What is the general form of a square root function?

Back

\( y = a\sqrt{x - h} + k \)

Front

What is the range of the function \( y = -\sqrt{x} \)?

Back

\((-\infty, 0]\)

Front

Define a square root function.

Back

A function of the form \( y = \sqrt{x} \) where the output is the non-negative square root of the input.

Front

What effect does a negative sign in front of a square root function have?

Back

It reflects the graph across the x-axis.

Front

What is the vertex of a square root function in the form \( y = a\sqrt{x - h} + k \)?

Back

The vertex is at the point \( (h, k) \).

Front

How does the value of \( a \) affect the graph of a square root function?

Back

If \( a > 1 \), the graph is vertically stretched; if \( 0 < a < 1 \), it is vertically compressed.

Front

What is the range of the function \( y = \sqrt{x} \)?

Back

\([0, \infty)\)