Question

Is the function Y=4|x²| positive, negative, increasing or decreasing? What is the end behavior of the function?

1) Positive and increasing, end behavior is upward
2) Positive and decreasing, end behavior is upward
3) Negative and increasing, end behavior is downward
4) Negative and decreasing, end behavior is downward

Answer 1

The function Y=4|x²| is always positive and neither increasing nor decreasing except at the vertex x=0. It is constant on both sides of the vertex with an upward end behavior.

Step-by-step explanation:

The function Y=4|x²| is always positive, regardless of the value of x, because the absolute value of x² is always non-negative, and when multiplied by 4, it remains positive. The function is neither increasing nor decreasing; it is constant with respect to x when x is not zero. However, at x=0, there is a vertex (a point where the direction of the graph changes), and the function transitions from constant on both sides of the vertex. Regarding the end behavior, as x goes to infinity or negative infinity, the function will also go to infinity. Hence, the end behavior of the function is upward.