Question

consider the graph. the graph is not one - to - one. it is neither and select choice. the graph has select choice x - intercept(s) and select choice y - intercept(s). the graph is select choice. the graph has maximum. as x→∞,y→ - ∞ as x→ - ∞,y→ - ∞

Explanation:

Step1: Determine even - odd nature

A function is even if \(f(x)=f( - x)\) (symmetric about y - axis) and odd if \(f(-x)=-f(x)\) (symmetric about origin). The given graph is neither symmetric about y - axis nor about the origin, so it is neither even nor odd.

Step2: Find x - intercepts

The x - intercepts are the points where the graph crosses the x - axis. The graph crosses the x - axis at 3 points, so it has 3 x - intercepts.

Step3: Find y - intercepts

The y - intercept is the point where the graph crosses the y - axis. The graph crosses the y - axis at 1 point, so it has 1 y - intercept.

Step4: Determine function type

The graph is a polynomial function as it is a smooth and continuous curve.

Answer:

It is neither (even nor odd) and (neither even nor odd).
The graph has 3 x - intercept(s) and 1 y - intercept(s).
The graph is a polynomial function.
The graph has maximum.
As \(x\to\infty,y\to-\infty\) As \(x\to-\infty,y\to-\infty\)