Help my math friends?

Question

In interval notation, what is the domain of f(x) = 2x^3 – 4x – 7?

a. x ∈ [-∞, ∞]

b. x ∈ (-∞, ∞)

c. f(x) ∈ [-7, ∞)

d. The range cannot be determined

In interval notation, what is the domain of f(x)=cube root of x?

a. x ∈ (-∞, 0) ∪ (0, ∞)

b. x ∈ (-∞, 0] ∪ [0, ∞)

c. x ≠ 0

d. x ∈ (-∞, ∞)

Over what interval of the domain is this function neither increasing nor decreasing: f(x) = x^2 + 4?

a. x = [0]

b. x ∈ (-∞, 0)

c. x ∈ (0, ∞)

d. f(x) ∈ (4, ∞)

Over what interval of the domain is this function decreasing: f(x) = x + 4?

a. x ∈ (-∞, 4)

b. x ∈ (-∞, ∞)

c. x ∈ (-4, ∞)

d. Never

Answer 1

1.  f(x) = 2x^3 – 4x – 7 is defined for all real numbers x. Domain is answer b.

2. f(x) = cube root of x is also defined for all real x. Domain is answer d.

3. f(x) = x^2 + 4 is a parabola opening upwards with axis of symmetry x=0. It is decreasing on (-∞, 0) and increasing on (0, ∞). The interval of the domain where it is neither increasing nor decreasing is answer a. x = [0]

4. f(x) = x + 4 is a straight line with slope 1 and y-intercept (0,4). Positive slope implies it is an increasing function for all real x. Answer d.