Which of the following functions does not have a domain of all real numbers?

1. y = √x + 5
2. y = 5x + 10
3. y = 2^{x − 4}
4. y = 3x² + 5x − 10

A
Correct! The square root function has a domain restriction, since you cannot take the square root of a negative number.

B
Incorrect. This is a linear function, and linear functions do not have domain restrictions.

C
Incorrect. This is an exponential function, and exponential functions do not have domain restrictions.

D
Incorrect. This is a quadratic function, and quadratic functions do not have domain restrictions.

A
Incorrect. The denominator of a rational function cannot be equal to zero.

B
Incorrect. The denominator of a rational function cannot be equal to zero.

C
Incorrect. Rational functions have a horizontal asymptote.

D
Correct!

A
Incorrect. This is set notation for all real numbers.

B
Incorrect. This is interval notation.

C
Correct! The domain of this exponential function is all real numbers.

D
Incorrect. This is inequality notation.

What is the domain and range of the function g(x) = √2x − 8?

1. Domain: (4, ∞), Range: (0, ∞)
2. Domain: (4, ∞), Range: (-∞, ∞)
3. Domain: [4, ∞), Range: (-∞, ∞)
4. Domain: [4, ∞), Range: [0, ∞)

A
Incorrect. The ordered pair (4, 0) is also a point included in g(x).

B
Incorrect. The range is also restricted because of the domain restrictions of the square root function.

C
Incorrect. The range is also restricted because of the domain restrictions of the square root function.

D
Correct!