Graphing Square and Cube Roots with Transformations

The video tutorial covers the process of graphing functions using transformations. It begins with an introduction to parent functions and transformations, followed by a detailed explanation of the steps involved in graphing. The tutorial includes three examples: a square root function, a cube root function, and a function with multiple transformations. Each example demonstrates how to identify transformations, graph the function, and determine the domain and range.

What is the first step in graphing a function with transformations?

• Determine the range

• Identify the transformations

• Determine the domain

• Draw the parent function

In Example 1, what does the transformation attached to the minus 5 indicate?

• Move up 5

• Move right 5

• Move down 5

• Move left 5

What is the domain of the function in Example 1 after the transformation?

• Negative infinity to 0

• 5 to infinity

• Negative infinity to 5

• 0 to infinity

In Example 2, what is the parent function used?

• Square root function

• Cube root function

• Linear function

• Quadratic function

What happens to the domain and range of the cube root function after the transformation in Example 2?

• Domain changes, range remains the same

• Range changes, domain remains the same

• Both domain and range change

• Both domain and range remain the same

In Example 3, what does the transformation outside the square root function indicate?

• Move left

• Compress or stretch

• Move up or down

• Move right

How does the transformation 'down three' affect the range of the function in Example 3?

• Range starts at 0 and goes to infinity

• Range starts at -3 and goes to infinity

• Range starts at 3 and goes to infinity

• Range starts at -3 and goes to 3

What is the effect of the 'squish' transformation in Example 3?

• Stretch vertically

• Compress vertically

• Move right

• Move left

What is the general rule for the domain of a square root function after a horizontal transformation?

• h to infinity

• Negative infinity to 0

• k to infinity

• 0 to infinity

What is the general rule for the range of a square root function after a vertical transformation?

• h to infinity

• Negative infinity to 0

• 0 to infinity

• k to infinity