Finding the Domain of Functions with Radicals and Fractions

The video tutorial explains how to determine the domain of various types of functions, including linear, polynomial, rational, and square root functions. It covers the use of interval notation and the importance of ensuring the denominator is not zero in rational functions. The tutorial also discusses how to handle square root functions, emphasizing the need to avoid negative numbers under even-indexed radicals. Additionally, it addresses complex cases involving fractions with square roots in both the numerator and denominator, using sign tests and number lines to find valid domains.

What is the domain of a linear function like 2x - 7?

• All negative numbers

• All positive numbers

• All integers

• All real numbers

For a polynomial function such as 2x^3 - 5x^2 + 7x - 3, what is the domain?

• All real numbers

• All positive numbers

• All negative numbers

• All integers

In the function 5/(x-2), which value is excluded from the domain?

• x = 5

• x = -2

• x = 2

• x = 0

How do you represent the domain of 5/(x-2) in interval notation?

• (-∞, 2) ∪ (2, ∞)

• (-∞, 2]

• [2, ∞)

• (-∞, ∞)

For the function 3x - 8 / (x^2 - 9x + 20), which values are excluded from the domain?

• x = 3 and x = 4

• x = 4 and x = 5

• x = -4 and x = -5

• x = 2 and x = 3

What is the domain of the function √(x - 4)?

• x ≥ 4

• x > 4

• x ≤ 4

• x < 4

For the function √(x^2 + 3x - 28), which intervals are included in the domain?

• (-∞, -7) ∪ (4, ∞)

• (-∞, -7] ∪ [4, ∞)

• (-7, 4]

• (-7, 4)

If a square root is in the denominator, how do you set the inside of the square root?

• Greater than zero

• Less than zero

• Less than or equal to zero

• Greater than or equal to zero

For the function √(x + 3) / (x^2 - 16), what is the domain?

• x < -4

• x > -3

• x ≥ -3 and x ≠ ±4

• x > 4

When dealing with fractions that have square roots in both the numerator and denominator, what is the key step?

• Set both parts greater than zero

• Find the intersection of the number lines

• Ignore the square roots

• Set both parts less than zero