Question

a regular hexagon can be represented as a function of the side - length, s, of the hexagon. $a(s)=\frac{3sqrt{3}}{2}s^{2}$. which statement is true? 1. the function is an increasing straight line. 2. the function is shaped like a square root function. 3. the function increases quadratically as s increases.

Explanation:

Step1: Identify the function type

The area function of the regular hexagon is $A(s)=\frac{3\sqrt{3}}{2}s^{2}$, which is a quadratic - function in the form of $y = ax^{2}$ where $a=\frac{3\sqrt{3}}{2}$.

Step2: Analyze the properties of quadratic functions

For a quadratic function $y = ax^{2}$ with $a>0$, as the independent variable $x$ (in this case $s$) increases, the function value $y$ (in this case $A(s)$) increases quadratically.

Answer:

The function $A(s)$ increases quadratically as $s$ increases.