Question

complex numbers and square roots
the graph of the function ( f(x) = \frac{4}{5}sqrt{x} ) is shown.
what is the domain of the function?
options:
all real numbers
all real numbers greater than or equal to 0
all real numbers less than or equal to 0
all real numbers greater than but not equal to 0

Explanation:

Step1: Recall domain of square root function

The function is \( f(x)=\frac{4}{5}\sqrt{x} \). For a square root function \( \sqrt{x} \), the expression inside the square root (radicand) must be non - negative, i.e., \( x\geq0 \).

Step2: Analyze the graph

Looking at the graph, the curve starts at \( x = 0 \) (the origin) and moves to the right (increasing \( x \)-values). This also indicates that \( x \) takes values from 0 (inclusive) to positive real numbers. So the domain is all real numbers greater than or equal to 0.

Answer:

all real numbers greater than or equal to 0 (matching the option "all real numbers greater than or equal to 0")