Question

You are describing the graph of a quintic function to someone who cannot see the graph. Which one of these statements would you use to describe it? End behaviours are x→[infinity],y→−[infinity] and x→−[infinity],y→[infinity],4 factors, and 0 turning points End behaviours are x→[infinity],y→[infinity] and x→−[infinity],y→−[infinity],4 factors, and 4 turning points End behaviours are x→±[infinity],y→−[infinity], zero x-intercepts, 1 turning point

Answer 1

The graph of a quintic function can be described based on its end behaviors, factors, and turning points. A quintic function with a negative leading coefficient will have the end behaviors of descending as x approaches positive infinity and ascending as x approaches negative infinity. It can have up to 4 turning points.

Step-by-step explanation:

To describe the graph of a quintic function for someone who cannot see it, one must consider end behaviors, factors, and turning points. If the end behaviors of the function are described as x→infinity, y→−infinity and x→−infinity, y→infinity, it suggests that the function ultimately descends as x grows positive and ascends as x becomes more negative. This behavior is indicative of a quintic function with a negative leading coefficient. The mention of 4 factors indicates that the function can be divided into 4 linear or irreducible quadratic expressions. However, the statement about 0 turning points seems inconsistent with a quintic function since quintic functions can have up to 4 turning points. The correct statement regarding turning points should be that a quintic function can have up to 4 turning points. It is also essential to note that a quintic polynomial function with four factors might indeed have fewer than four turning points if some of the roots (factors) are complex or if multiple roots coincide, but it would not have zero turning points.