Graphing Radical Functions

Front

What is the parent function of a radical function?

Back

The parent function of a radical function is f(x) = √x.

Front

What does it mean to shift a graph to the right?

Back

Shifting a graph to the right means adding a positive value to the x-variable in the function, resulting in a horizontal translation.

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means multiplying the function by -1, which flips the graph vertically.

Front

How do you determine the range of a radical function?

Back

The range of a radical function is determined by the lowest point on the graph and extends to positive infinity.

Front

What transformation is represented by f(x) = √(x - 3)?

Back

This transformation shifts the graph of the parent function 3 units to the right.

Front

What transformation is represented by f(x) = -√x + 2?

Back

This transformation reflects the graph over the x-axis and shifts it up 2 units.

Front

How do you identify the vertex of a transformed radical function?

Back

The vertex can be identified from the function in the form f(x) = a√(x - h) + k, where (h, k) is the vertex.

Front

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

Back

A negative sign in front of a radical function reflects the graph over the x-axis.

Front

What does the notation [ -2, ∞ ) signify in terms of range?

Back

It signifies that the range includes all values from -2 to positive infinity, including -2.

Front

How does the transformation f(x) = √(x + 4) affect the graph?

Back

This transformation shifts the graph 4 units to the left.