Understanding Domain of Functions

What is the domain of the function f(x) = 2x - 5?

• x ≠ 0

• x < 0

• All real numbers

• x > 0

For the function with a fraction, what must be avoided to ensure the domain is valid?

• Positive numbers

• Complex numbers

• Zero in the denominator

• Negative numbers

When dealing with square root functions, what condition must be met for the domain?

• The value under the root must be zero

• The value under the root must be a fraction

• The value under the root must be negative

• The value under the root must be positive or zero

In a function with both a fraction and a square root, what two conditions must be met?

• The denominator must be negative and the root must be zero

• The denominator must be zero and the root must be negative

• The denominator must not be zero and the root must be positive or zero

• The denominator must be positive and the root must be negative

What is the domain of the function f(x) = (x + 2) / √(4 - 2x)?

• x ≠ 2

• x = 2

• x > 2

• x < 2

For a quadratic function in the denominator, what must be avoided?

• The quadratic must be a fraction

• The quadratic must be positive

• The quadratic must be zero

• The quadratic must be negative

What is the domain of the function f(x) = 1 / (x^2 - 7x + 10)?

• x = 5 and x = 2

• x ≠ 5 and x ≠ 2

• x > 5 and x > 2

• x < 5 and x < 2

In the final example, what is the domain of the function with a square root and fraction?

• x > 1 and x < 3

• x < 1 and x > 3

• x ≤ 1 and x = 3

• x ≥ 1 and x ≠ 3

What is the interval notation for the domain of a function where x ≥ 1 and x ≠ 3?

• (1, 3) ∪ [3, ∞)

• [1, 3) ∪ (3, ∞)

• [1, ∞)

• (1, ∞)

What is a key takeaway from the video regarding domain restrictions?

• Always avoid positive values in the function

• Always avoid zero in the denominator and negative values under even roots

• Always include zero in the denominator

• Always allow negative values under even roots