Question

consider the graph of ( g(x) )
which statement is true? select all that apply.
a. the domain is all real numbers
b. the range is all real numbers
c. the domain is ( x geq 0 )
d. the range is ( f(x) geq 0 )

Explanation:

Step1: Analyze the domain

The graph extends infinitely left and right along the x-axis, so all real x are allowed.

Step2: Analyze the range

The graph has two rays: one going infinitely upward (positive y-values) and one going infinitely downward (negative y-values), covering all real y-values.

Step3: Evaluate each option

• A: Domain is all real numbers (matches Step1).
• B: Range is all real numbers (matches Step2).
• C: Domain is $x\geq0$ (false, graph includes negative x).
• D: Range is $g(x)\geq0$ (false, graph includes negative y).

Answer:

A. The domain is all real numbers
B. The range is all real numbers