Graphing Cube Root Functions Using Transformations

This lesson covers graphing key root functions using transformations. It reviews inverse functions, explaining how they switch domain and range and are reflections over the line y=x. The lesson also discusses rigid and nonrigid transformations, which affect the graph's shape and position. It explains how to graph cube root functions by using a t-table and switching domain and range. The domain and range of cube root functions are all real numbers. Finally, the lesson demonstrates graphing h(x) using transformations, including vertical stretching and horizontal shifting, and states the domain and range.

What is the result of switching the x and y in the equation y = 2x + 3 and solving for y?

• y = 2x + 3

• y = 1/2x - 3/2

• y = 1/2x + 3/2

• y = 2x - 3

Which of the following is true about the domain of the cube root function?

• It includes only integers.

• It includes only negative real numbers.

• It includes all real numbers.

• It includes only positive real numbers.

How does a vertical stretch affect the graph of a function?

• It shifts the graph horizontally.

• It shifts the graph vertically.

• It compresses the graph horizontally.

• It changes the shape by stretching it vertically.

What is the effect of adding 1 to the x inside the cube root function?

• It shifts the graph to the left by 1 unit.

• It compresses the graph horizontally.

• It stretches the graph vertically.

• It shifts the graph to the right by 1 unit.

What is the range of the function h(x) = 2 * cube root of x + 1?

• Negative infinity to positive infinity

• Zero to positive infinity

• Negative infinity to zero

• One to positive infinity