Question

over the interval -1 < x < 2, the graph of the polynomial shown could be described as
1 quadratic
2 increasing
3 complex
4 decreasing

Explanation:

Step1: Analyze each option

• Option 1 (quadratic): A quadratic function is a polynomial of degree 2, which has a parabola as its graph (at most one turning point). The given graph has multiple turning points, so it's not quadratic.
• Option 2 (increasing): To check if a function is increasing on an interval, we see if as \( x \) increases, \( y \) also increases. Over \( -1 < x < 2 \), let's look at the graph: at \( x = -1 \), \( y = -9 \); then as \( x \) moves towards 2, the \( y \)-values go from -9, cross the axis, and at \( x = 2 \), \( y = 1 \). So as \( x \) increases from -1 to 2, \( y \) increases from -9 to 1. So the function is increasing here.
• Option 3 (complex): "Complex" is not a term used to describe the behavior of a polynomial graph over an interval. Polynomial graphs are real - valued here, so this is incorrect.
• Option 4 (decreasing): If the function were decreasing, as \( x \) increases, \( y \) would decrease. But we saw that from \( x=-1 \) ( \( y = -9 \)) to \( x = 2 \) ( \( y = 1 \)), \( y \) increases, so it's not decreasing.

Answer:

1. increasing