Solving Square/Cube Root Equations and Transformations

Front

What is a square root?

Back

A square root of a number x is a value y such that y² = x. For example, the square root of 9 is 3, since 3² = 9.

Front

What is a cube root?

Back

A cube root of a number x is a value y such that y³ = x. For example, the cube root of 27 is 3, since 3³ = 27.

Front

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

Back

Reflecting a function over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What does it mean to reflect a function over the y-axis?

Back

Reflecting a function over the y-axis means that for every point (x, y) on the graph, the point (-x, y) will also be on the graph.

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

What is a vertical compression of a function?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter.

Front

What does a horizontal shift to the right mean?

Back

A horizontal shift to the right means that the entire graph of the function moves to the right by a certain number of units.

Front

What does a horizontal shift to the left mean?

Back

A horizontal shift to the left means that the entire graph of the function moves to the left by a certain number of units.

Front

Back

Front

Back

The starting point is (-2, -8). This is found by identifying the transformations applied to the basic square root function.