Graphing Radicals Homework Day 2

Front

What is the general form of a square root function?

Back

y = √(x - h) + k, where (h, k) is the vertex of the graph.

Front

How does the graph of y = √(x) change when we add a constant to x?

Back

The graph shifts horizontally. For example, y = √(x + 3) shifts left by 3 units.

Front

What effect does adding a constant outside the square root have on the graph?

Back

It shifts the graph vertically. For example, y = √(x) + 3 shifts the graph up by 3 units.

Front

What is the vertex of the function y = √(x - 4) - 2?

Back

The vertex is (4, -2).

Front

Describe the transformation of the graph of y = √(x) to y = √(x - 2).

Back

The graph shifts right by 2 units.

Front

What is the domain of the function y = √(x - 3)?

Back

The domain is x ≥ 3.

Front

What is the range of the function y = √(x) + 3?

Back

The range is y ≥ 3.

Front

How do you identify the transformations of the function y = -√(x + 4) - 2?

Back

The graph reflects over the x-axis, shifts left by 4 units, and shifts down by 2 units.

Front

What is the effect of a negative sign in front of the square root function?

Back

It reflects the graph over the x-axis.

Front

How do you graph y = √(x) - 3?

Back

Start with the graph of y = √(x) and shift it down by 3 units.