graphing square roots and cube roots

Front

What is the general form of a square root function?

Back

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

Front

How does the graph of f(x) = √(x) differ from f(x) = √(x - 4)?

Back

The graph of f(x) = √(x - 4) is shifted 4 units to the right.

Front

What is the effect of the '-2' in the function f(x) = √(x - 4) - 2?

Back

It shifts the graph down by 2 units.

Front

What is the domain of the function f(x) = √(x - 4)?

Back

The domain is x ≥ 4.

Front

What is the range of the function f(x) = √(x - 4)?

Back

The range is y ≥ 0.

Front

What type of function is f(x) = -√(x + 1)?

Back

It is a square root function reflected over the x-axis.

Front

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

Back

The vertex is at the point (-4, -2).

Front

What transformation does the function f(x) = √(x + 4) - 2 represent?

Back

It represents a left shift of 4 units and a downward shift of 2 units.

Front

What is the effect of a negative sign in front of a square root function, such as in f(x) = -√(x)?

Back

It reflects the graph over the x-axis.

Front

What is the significance of the 'h' and 'k' in the vertex form of a square root function?

Back

They represent horizontal and vertical shifts of the graph, respectively.