Polynomial and Rational Functions Concepts

This video tutorial focuses on multiple choice questions related to rational and polynomial functions from the AP Pre-Calculus exam. It covers the end behavior of polynomial functions, constructing functions with specific properties, determining the domain of rational functions, analyzing graphs for zeros and multiplicity, and using a calculator to solve problems involving rational functions. The tutorial emphasizes understanding the concepts and applying them to solve exam-style questions effectively.

What percentage of the AP Pre-Calculus exam's multiple-choice questions cover polynomial and rational functions?

• 10-15%

• 20-25%

• 40-45%

• 30-35%

Which of the following statements is true about the end behavior of the polynomial function p(x) = -4x^5 + 3x^2 + 1?

• Both ends go towards negative infinity.

• Both ends go towards positive infinity.

• The left end goes towards positive infinity and the right end goes towards negative infinity.

• The left end goes towards negative infinity and the right end goes towards positive infinity.

If a function has a zero at x = 3, a vertical asymptote at x = 2, and a hole at x = 1, which of the following could be the function?

• (x-3)(x-1)/(x-2)(x-1)

• (x-3)/(x-2)

• (x-3)(x-2)/(x-1)

• (x-3)(x-2)(x-1)

What is the domain of the function K(x) = (x^2 - 2x - 35) / (x^3 - 3x^2 - 18x)?

• All real numbers except -3, 0, and 6

• All real numbers except -3 and 6

• All real numbers except 0 and 6

• All real numbers except -3 and 0

What is the first step in determining the domain of a rational function?

• Set the denominator equal to zero

• Set the numerator equal to zero

• Factor the numerator

• Factor the denominator

In the function K(x) = (x^2 - 2x - 35) / (x^3 - 3x^2 - 18x), which values must be excluded from the domain?

• Values that make the function undefined

• Values that make the numerator zero

• Values that make both numerator and denominator zero

• Values that make the denominator zero

Which of the following could be an expression for a polynomial function G(x) with zeros at -a, b, and c, where the zero at c has an even multiplicity?

• (x+a)(x-b)(x-c)^2

• (x-a)(x+b)(x-c)

• (x+a)(x-b)(x-c)

• (x-a)(x+b)(x-c)^2

When using a calculator to find the intersection points of a function, which command is used?

• Zoom

• Intersect

• Trace

• Calculate

What is the purpose of adjusting the window settings on a graphing calculator?

• To zoom in on a specific part of the graph

• To change the color of the graph

• To change the scale of the axes

• To ensure the entire function is visible

How many hours did it take for the temperature to increase from 0 degrees to 5 degrees in the given problem?

• 4.28 hours

• 3.28 hours

• 2.28 hours

• 1.28 hours