Question

State the domain and range of each function. Explain your thinking. a. f(x)=−3√2x+8 −1

Answer 1

The domain of the function is x ≥ -4 and the range is (-∞, -1].

Step-by-step explanation:

The domain of a function refers to the set of all possible input values, while the range refers to the set of all possible output values. For the function f(x) = -3√(2x + 8) - 1, let's determine the domain and range:

Domain:

• The expression inside the square root, 2x + 8, must be non-negative since the square root of a negative number is undefined.
• Solving 2x + 8 ≥ 0, we get x ≥ -4. Hence, the domain is x ≥ -4.

Range:

• The square root of any non-negative number will always yield a real number, so there are no restrictions on the range.
• The range of this function is (-∞, -1].

Therefore, the domain is x ≥ -4 and the range is (-∞, -1].