T Misconceptions Implied Domain

The video addresses common misconceptions about implied domain in functions. It provides counterexamples to false statements, such as the belief that all functions have a maximum of two domain restrictions. The video explains the differences between holes and vertical asymptotes, emphasizing that the domain remains unchanged. It also clarifies that not all rational functions have domain restrictions, using examples like x^2 + 4. Finally, it discusses the domain of radical functions, highlighting the differences between even and odd roots.

What is a common misconception about the number of domain restrictions a function can have?

• Functions cannot have any domain restrictions.

• Functions can have unlimited domain restrictions.

• Functions can have a maximum of two domain restrictions.

• Functions can have only one domain restriction.

How does the domain of a function change when a discontinuity is a hole compared to a vertical asymptote?

• The domain is different for holes and vertical asymptotes.

• The domain is undefined for both cases.

• The domain is the same for both holes and vertical asymptotes.

• The domain only changes for vertical asymptotes.

Which of the following statements is true about rational functions?

• All rational functions have domain restrictions.

• Rational functions always have a hole in their domain.

• Some rational functions have no domain restrictions.

• Rational functions never have vertical asymptotes.

What is the domain of a function with an even root?

• Values where the radicand is non-negative

• Only positive numbers

• Values where the radicand is negative

• All real numbers

How does the domain of a function with an odd root differ from one with an even root?

• Both have the same domain restrictions.

• Odd roots have a restricted domain.

• Odd roots have no domain restrictions.

• Even roots have no domain restrictions.

What happens to the domain of a function if the radicand of an even root is always positive?

• The domain is restricted to positive numbers.

• The domain is all real numbers.

• The domain is restricted to negative numbers.

• The domain is undefined.

Which of the following is true about the domain of a cube root function?

• It is restricted to positive numbers.

• It is restricted to negative numbers.

• It includes all real numbers.

• It is undefined.