Graphing Radical Functions

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical, such as a square root, cube root, etc. The general form is y = √(x) or y = n√(x).

Front

What does the equation y = √(x) represent?

Back

The equation y = √(x) represents the basic square root function, which starts at the origin (0,0) and increases to the right.

Front

How does the equation y = √(x - 2) transform the graph of y = √(x)?

Back

The equation y = √(x - 2) shifts the graph of y = √(x) to the right by 2 units.

Front

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

Back

Adding a constant outside the radical, such as in y = √(x) + 2, shifts the graph vertically upwards by that constant.

Front

What does the equation y = √(x + 1) - 2 do to the graph of y = √(x)?

Back

The equation y = √(x + 1) - 2 shifts the graph left by 1 unit and down by 2 units.

Front

What is the transformation of the graph for y = -√(x)?

Back

The graph of y = -√(x) reflects the graph of y = √(x) over the x-axis.

Front

How do you identify the vertex of a radical function?

Back

The vertex of a radical function in the form y = √(x - h) + k is the point (h, k).

Front

What does the term 'horizontal shift' refer to in graph transformations?

Back

A horizontal shift refers to moving the graph left or right along the x-axis, determined by the value added or subtracted from x.

Front

What does the term 'vertical shift' refer to in graph transformations?

Back

A vertical shift refers to moving the graph up or down along the y-axis, determined by the value added or subtracted from the function.

Front

What is the effect of the equation y = √(x - 5) - 1 on the graph of y = √(x)?

Back

The equation y = √(x - 5) - 1 shifts the graph right by 5 units and down by 1 unit.