Question

what is the domain of the following quadratic function? f(x) = 3x² + 4x - 2 a) x ≥ -2 b) x ≤ -2 c) all real #s d) x ≥ -2/3

Explanation:

Step1: Recall domain of quadratic functions

Quadratic functions are polynomials of degree 2, and the domain of a polynomial function (including linear, quadratic, cubic, etc.) is all real numbers because there are no restrictions (like division by zero or square roots of negative numbers) on the input \( x \) for any real number \( x \). The function given is \( f(x)=3x^{2}+4x - 2 \), which is a quadratic (polynomial) function.

Step2: Analyze the options

• Option A: \( x\geq - 2 \) is incorrect because there is no restriction that \( x \) must be greater than or equal to - 2.
• Option B: \( x\leq - 2 \) is incorrect as there is no upper - bound or lower - bound restriction like this for a quadratic function.
• Option C: "All real #s" is correct because for any real number \( x \), we can compute \( 3x^{2}+4x - 2 \).
• Option D: \( x\geq-\frac{2}{3} \) is incorrect as there is no such restriction on the input \( x \) for this quadratic function.

Answer:

C) All real #s