Determine inverse of a quadratic equation then determine domain and range

The video tutorial explains how to identify the domain of a function by checking for restrictions like division by zero or taking the square root of a negative number. It then describes finding the range by determining the inverse of the function, swapping variables, and solving for Y. The importance of considering both positive and negative square roots is highlighted. Finally, the domain of the inverse function is determined, which corresponds to the range of the original function, and a graphical representation is suggested.

What is a key restriction to consider when identifying the domain of a function?

• The function must have a positive slope.

• The function must be continuous.

• The function must be differentiable.

• The function cannot divide by zero.

When finding the inverse of a function, what must you remember to include when introducing a square root?

• Only the positive square root.

• Neither, just the absolute value.

• Both positive and negative square roots.

• Only the negative square root.

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

• The domain of the inverse is the opposite of the range of the original.

• They are unrelated.

• The domain of the inverse is the range of the original.

• The domain of the inverse is the same as the domain of the original.

What condition must be met for the expression under a square root in a function's inverse?

• It must be equal to zero.

• It must be greater than or equal to zero.

• It must be greater than zero.

• It must be less than zero.

How does a vertical reflection affect the domain of a function?

• It changes the domain completely.

• It has no effect on the domain.

• It doubles the domain.

• It halves the domain.