Graph Inverse Function by adding restrictions

The video tutorial covers the concepts of implied and restricted domains in functions, explaining how they are used in mathematical contexts and word problems. It discusses the process of finding inverse functions and the importance of applying restrictions to ensure they remain functions. The tutorial also includes graphing techniques for functions and their inverses, highlighting transformations such as shifts and reflections.

What is the primary difference between an implied domain and a restricted domain?

• Implied domain is always larger than restricted domain.

• Implied domain only applies to quadratic functions.

• Implied domain is defined by the function itself, while restricted domain is an additional constraint.

• Restricted domain is defined by the function itself, while implied domain is an additional constraint.

In word problems, why are restricted domains often used?

• To include negative values.

• To simplify calculations.

• To focus on realistic scenarios, like positive time or length.

• To make the problem more complex.

What is a common characteristic of restricted domains in real-world scenarios?

• They are always infinite.

• They often involve only positive values.

• They focus on non-real numbers.

• They include negative values.

What does the vertical line test determine about a function?

• Whether a graph represents a function.

• Whether a function is continuous.

• Whether a function is differentiable.

• Whether a function is one-to-one.

Why might a function's inverse not be a function?

• It is not differentiable.

• It is not continuous.

• It fails the vertical line test.

• It fails the horizontal line test.

How can you ensure that the inverse of a quadratic function is also a function?

• By ensuring the function is linear.

• By applying the horizontal line test.

• By using only negative y-values.

• By restricting the domain to positive x-values.

What transformation is applied to a quadratic function to obtain its inverse as a square root function?

• Vertical shift

• Horizontal shift

• Reflection over the x-axis

• Reflection over the y-axis