Understanding Domains of Radical Functions

This video tutorial explains how to find the domain of radical functions without using graphs. It covers examples of square roots, rational functions, and quadratic functions inside radicals. The tutorial also discusses the differences between even and odd index radicals, highlighting how the domain is affected. Through various examples, the video demonstrates how to use number lines and inequalities to determine the domain of different functions.

What is the domain of the function f(x) = √(4 + x)?

• [-4, ∞)

• (-∞, -4]

• [4, ∞)

• (-∞, 4]

For the function g(x) = 1/√(x + 4), what is the correct domain?

• [4, ∞)

• (-4, ∞)

• [-4, ∞)

• (-∞, -4)

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

• It remains the same

• It changes direction

• It becomes undefined

• It becomes zero

In the context of domains, what does an open circle on a number line indicate?

• The value is zero

• The value is excluded

• The value is negative

• The value is included

How do you determine the domain of a function with a quadratic inside a radical?

• By setting the quadratic less than zero

• By setting the quadratic not equal to zero

• By setting the quadratic greater than zero

• By setting the quadratic equal to zero

What is the domain of the function f(x) = √(x^2 + 3x - 4) when the radical is in the numerator?

• (-∞, -4) ∪ (1, ∞)

• (-∞, 4) ∪ (1, ∞)

• (-∞, -4] ∪ [1, ∞)

• (-∞, 4] ∪ [1, ∞)

What is the domain of the function h(x) = √(x^2 + 3x - 4) when the radical is in the denominator?

• (-∞, -4) ∪ (1, ∞)

• (-∞, -4] ∪ [1, ∞)

• (-∞, 4) ∪ (1, ∞)

• (-∞, 4] ∪ [1, ∞)

What is the domain of a cube root function?

• Only non-negative numbers

• Only positive numbers

• All real numbers

• Only negative numbers

For the function f(x) = √(x^2 + 3x - 4), what is the domain if the index is even?

• (-∞, 4) ∪ (1, ∞)

• (-∞, 4] ∪ [1, ∞)

• (-∞, -4] ∪ [1, ∞)

• (-∞, -4) ∪ (1, ∞)

What is the domain of the function f(x) = √(1 + x)(5 - x) when the index is even?

• (-∞, 1) ∪ (5, ∞)

• (-1, 5)

• [-1, 5]

• (-∞, -1) ∪ (5, ∞)