Question

josé attends victory high school, home of the fighting vs. he wants to create a computer program that will send \vs\ flying all around the monitor. josé decides he can use algebra to simulate the shape and motion. which of the following functions would be best for josé to use to simulate a \v\ shape?
$f(x)=x^{2}$
$f(x)=x$
$f(x)=|x|$
$f(x)=\sqrt{x}$
$f(x)=x^{3}$

Explanation:

Step1: Analyze the shape of each function

• For \(f(x)=x^{2}\), it is a parabola opening upwards. Its graph is U - shaped.
• For \(f(x)=x\), it is a straight - line passing through the origin with a slope of 1.
• For \(f(x)=\vert x\vert\), when \(x\geq0\), \(f(x)=x\); when \(x < 0\), \(f(x)=-x\). The graph of \(y = \vert x\vert\) has a "V" - shape with the vertex at the origin \((0,0)\).
• For \(f(x)=\sqrt{x}\), the domain is \(x\geq0\), and its graph is a curve starting at the origin and increasing in the first quadrant.
• For \(f(x)=x^{3}\), it is an odd function. Its graph passes through the origin and has a different S - like shape for positive and negative \(x\) values.

Answer:

\(f(x)=\vert x\vert\)