Understanding Domains of Radical and Rational Functions

The video tutorial focuses on determining the domain of various functions, particularly those involving square roots and rational expressions. It explains how to handle functions with radicals in the numerator and denominator, and how to factor quadratic expressions to find critical points. The tutorial also covers plotting solutions on a number line and using interval notation to express domains. Through multiple examples, it demonstrates how to identify valid regions for the domain, ensuring no negative numbers are inside square roots and no zeros in denominators.

What is the domain of the function f(x) = √(x + 3)?

• x ≥ -3

• x > -3

• x < -3

• x ≤ -3

For a function with a radical in the denominator, what must be true about the expression inside the radical?

• It must be equal to zero

• It must be less than zero

• It must be greater than zero

• It can be any real number

When dealing with two radicals in a function, how do you determine the domain?

• Add the domains of both radicals

• Use the domain of the second radical only

• Use the domain of the first radical only

• Find the intersection of the domains of each radical

In a rational function without radicals, what is the main restriction on the domain?

• The function must be continuous

• The function must be differentiable

• The numerator cannot be zero

• The denominator cannot be zero

What is the domain of the function f(x) = 1/(x + 3)?

• x < -3

• x > -3

• x = -3

• x ≠ -3

How do you find the domain of a function that includes both a radical and a rational expression?

• Find the intersection of the domains of both

• Add the domains of both

• Only consider the rational expression

• Only consider the radical

What happens to the inequality when you divide both sides by a negative number?

• It becomes undefined

• It remains the same

• It changes direction

• It becomes an equality

If a function has a quadratic expression inside a radical, what is the first step to find the domain?

• Factor the quadratic expression

• Graph the quadratic function

• Solve the quadratic equation

• Differentiate the quadratic expression

In interval notation, what does a parenthesis indicate?

• The interval is infinite

• The endpoint is excluded

• The interval is finite

• The endpoint is included

For a function with a radical in the numerator, what type of circle is used on the number line for critical points?

• Open circle

• No circle

• Half circle

• Closed circle