Find the Domain with Restrictions | Part 2

The video tutorial explains domain restrictions in functions, focusing on square root and rational functions. It covers how to identify domains using algebraic expressions, graphs, and interval notation. The tutorial also explores cube root functions, emphasizing that they have no domain restrictions. Examples are provided to illustrate these concepts, helping students understand how to determine the domain of various functions.

What is the domain of the function F(x) = 2x^2 - 3?

• x ≠ 0

• All real numbers

• x < 0

• x > 0

For the function G(x) = sqrt(x - 5), which of the following is true about its domain?

• x < 5

• x ≥ 5

• x > 0

• x ≠ 5

How can the domain of a square root function be represented graphically?

• Using a solid line for excluded values

• Using a dashed line for excluded values

• Using an open circle for included values

• Using a filled circle for included values

What is the domain of the function H(x) = 1/(x - 4)?

• x < 4

• x ≠ 4

• x = 4

• x > 4

In interval notation, how is the domain of H(x) = 1/(x - 4) expressed?

• (4, ∞)

• [4, ∞)

• (-∞, 4]

• (-∞, 4) ∪ (4, ∞)

Which of the following is a valid domain for the function f(x) = sqrt(-2x + 7)?

• x < 7/2

• x ≤ 7/2

• x ≥ 7/2

• x > 7/2

For the function f(x) = 1/(1 - 2x), what value of x is not in the domain?

• x = 2

• x = -1/2

• x = 0

• x = 1/2

What is unique about the domain of cube root functions compared to square root functions?

• Cube roots have no domain restrictions

• Cube roots can only accept negative numbers

• Cube roots can only accept positive numbers

• Cube roots can accept both positive and negative numbers

Which of the following statements is true about cube root functions?

• They are only defined for negative numbers

• They are only defined for positive numbers

• They have the same domain restrictions as square root functions

• They can accept any real number as input

What is the domain of the function G(x) = cube root(x)?

• All real numbers

• x ≠ 0

• x > 0

• x < 0