How to find the inverse of functions by using restrictions

The video tutorial covers graph transformations, finding inverses, and domain restrictions. It explains how to sketch graphs, find inverses of functions, and restrict domains to ensure the inverse is a function. The tutorial also discusses analyzing quadratic functions and understanding domain and range, emphasizing the importance of correct notation and visualization.

What transformation is applied to the square root graph to reflect it about the Y-axis and shift it 4 units to the right?

• Reflect about the X-axis and shift 4 units right

• Reflect about the Y-axis and shift 4 units right

• Reflect about the Y-axis and shift 4 units left

• Reflect about the X-axis and shift 4 units left

When finding the inverse of a function, why is it important to consider domain restrictions?

• To ensure the inverse is a function

• To simplify the equation

• To avoid complex numbers

• To make the graph look symmetrical

What is the main issue with finding the inverse of a non-one-to-one function?

• The inverse is always undefined

• The inverse is not a function

• The inverse is always a linear function

• The inverse is always a quadratic function

Why is it necessary to choose between the positive and negative square root when finding an inverse?

• To avoid imaginary numbers

• To make the graph symmetrical

• To simplify the equation

• To ensure the inverse is a function

How can you determine the domain of a function from its graph?

• By looking at the range of the inverse

• By calculating the slope of the graph

• By identifying the x-values covered by the graph

• By identifying the y-values covered by the graph

What is the relationship between the domain of a function and the range of its inverse?

• They are unrelated

• The range of the function is the domain of the inverse

• The domain of the function is the range of the inverse

• They are always equal

What is the range of a function if its graph is entirely above the x-axis?

• Negative Infinity to 0

• 0 to Infinity

• Negative Infinity to Infinity

• 0 to 4