Question

what is the domain of the function represented by this graph?

\\(x \ge 4\\)

\\(-2 \le x \le 2\\)

all real numbers

\\(x \le 0\\)

Explanation:

Identify the function type from the graph

The graph shows a parabola opening upwards, which represents a quadratic function of the form:

$$y = ax^2 + bx + c$$

Determine the domain of a quadratic function

A quadratic function is a polynomial function. Polynomials are defined for all real values of \(x\). Looking at the graph, the curve extends infinitely to the left and to the right, meaning there are no restrictions on the input values.

$$\text{Domain} = (-\infty, \infty)$$

Match with the given options

The set of all valid inputs is represented by "all real numbers".

Answer:

• \(x \ge 4\)
• \(-2 \le x \le 2\)
• all real numbers (Correct answer)
• \(x \le 0\)