Inverse of a quadratic function with domain restriction

The video tutorial explains one-to-one functions, emphasizing that each X value must have a unique Y value. It introduces the horizontal line test to determine if a function is one-to-one. The tutorial discusses graphing with restrictions to find inverses and provides steps to calculate the inverse of a function. It also covers the relationship between the domain and range of functions and their inverses.

What is a key characteristic of a one-to-one function?

• Every X value has a unique Y value.

• Every Y value has multiple X values.

• Every X value has multiple Y values.

• Every Y value is zero.

Which test can be used to determine if a function is one-to-one?

• Slope test

• Derivative test

• Horizontal line test

• Vertical line test

What happens to the inverse of a function if the original function is not one-to-one?

• The inverse is also not a function.

• The inverse becomes a linear function.

• The inverse does not exist.

• The inverse is always a quadratic function.

How can the range of a function be determined if graphing is difficult?

• By using the vertical line test

• By using the domain of the inverse function

• By finding the slope

• By calculating the derivative

What is the domain of the inverse function if the range of the original function is 1 to Infinity?

• 0 to 1

• 1 to Infinity

• Negative Infinity to 0

• 0 to Infinity