Answer to Question #240870 in Calculus for CCW

Question

Unit 1 Review:

7) Use link below to answer questions

• Even or odd degree?
• Least possible degree?
• Number of turning points?
• Positive or negative leading coefficient?
• # of real zeros?
• Coordinate y intercept

Answer 1

The link is not present in the question, so I am defining all the terms related to the same.

Even degree: If a function is even, the graph is symmetrical about the y-axis. If the function is odd, the graph is symmetrical about the origin.

Even function: The mathematical definition of an even function is f(–x) = f(x) for any value of x.

Odd function: The mathematical definition of an odd function is f(–x) = -f(x) for any value of x.

Least possible degree:

Like any constant value, the value 0 can be considered as a (constant) polynomial, called the zero polynomial. It has no nonzero terms, and so, strictly speaking, it has no degree either. As such, its degree is usually undefined.

Turning Points:

Any polynomial of degree n can have a minimum of zero turning points and a maximum of n−1 .

Positive or Negative leading coefficient: If the leading coefficient is positive the function will extend to + ∞; whereas if the leading coefficient is negative, it will extend to - ∞.

Number of real zeroes: Regardless of odd or even, any polynomial of positive order can have a maximum number of zeros equal to its order.

y-intercept: The y-intercept is the point at which the graph crosses the y-axis. At this point, the x-coordinate is zero.