Master The Domain of Rational and Radical Functions

The video tutorial explains how to determine the domain of rational and radical functions. It covers the basic principles of identifying values that are part of the domain and those that are not, focusing on conditions like the denominator being zero in rational functions and the radicand being negative in radical functions. The tutorial provides multiple examples, including functions with radicals, quadratics, and rational expressions, demonstrating how to solve inequalities and use interval notation to express domains.

What is the main reason a value is excluded from the domain of a rational function?

• It makes the entire function negative.

• It makes the function undefined.

• It makes the denominator zero.

• It makes the numerator zero.

For the function y = sqrt(3 - 2x), what is the domain in interval notation?

• (-∞, 3/2]

• [3/2, ∞)

• (-∞, 3/2)

• [3/2, ∞]

When solving for the domain of a radical function, why must the expression under the radical be non-negative?

• To avoid imaginary numbers in the real number system.

• To ensure the function is increasing.

• To ensure the function is continuous.

• To make the function differentiable.

In the function sqrt(x^2 - 4), what are the critical points that determine the domain?

• 0 and 4

• -2 and 2

• -4 and 4

• -2 and 0

For the function sqrt(x^2 - 4), what is the domain in interval notation?

• (-2, 2)

• (-∞, -2) ∪ (2, ∞)

• (-∞, -2] ∪ [2, ∞)

• (-∞, 2] ∪ [2, ∞)

What is the primary concern when determining the domain of a rational function?

• The function being negative.

• The numerator being zero.

• The function being positive.

• The denominator being zero.

For the function with radicals in both numerator and denominator, what must be true about the denominator?

• It must be greater than zero.

• It must be non-negative.

• It must be less than zero.

• It must be equal to zero.

In the function with radicals in both numerator and denominator, what is the domain if the numerator is sqrt(x - 1) and the denominator is sqrt(3 - x)?

• [1, 3]

• (1, 3]

• (1, 3)

• [1, 3)

When dealing with a function that has both a radical and a rational component, what must be considered?

• Only the radical component.

• Neither component.

• Only the rational component.

• Both components separately.

For a function with multiple constraints, what is the best approach to find the domain?

• Consider each constraint separately and find the intersection.

• Find the union of all constraints.

• Consider only the constraint with the largest impact.

• Ignore the constraints and find the domain of the entire function.