Polynomial Functions and Their Properties

This video covers AP Precalculus Unit 1, focusing on polynomial and rational functions. It explains key concepts such as input-output values, rate of change, polynomial terminology, and end behavior. The video also introduces rational functions, asymptotes, and how to find zeros and holes. Additionally, it discusses transformations, constructing function models, and using calculators for modeling.

What are the two main types of functions covered in AP Precalculus Unit 1?

• Polynomial and Rational

• Trigonometric and Hyperbolic

• Exponential and Logarithmic

• Linear and Quadratic

In a function, what is the set of input values called?

• Range

• Domain

• Slope

• Intercept

What does a positive rate of change indicate about the relationship between two quantities?

• Both remain constant

• Both increase or decrease together

• One increases, the other decreases

• One remains constant

In a quadratic function, what does the average rate of change over an interval represent?

• Constant rate

• Rate of zero

• Slope of the secant line

• Slope of the tangent line

Which of the following is NOT a type of polynomial function covered in this course?

• Cubic

• Exponential

• Linear

• Quadratic

What is the term for the highest value of an exponent in a polynomial function?

• Intercept

• Degree

• Coefficient

• Root

What does the end behavior of a polynomial function describe?

• The intercepts of the graph

• The slope of the graph

• How the graph ends

• How the graph starts

What are the invisible lines that a rational function graph approaches but never touches?

• Vertices

• Asymptotes

• Intercepts

• Roots

How do you find the real zeros of a rational function?

• Set the numerator to zero

• Set the denominator to zero

• Set both numerator and denominator to zero

• Find the slope

What is a vertical asymptote in a rational function?

• A point where the graph crosses the x-axis

• A point where the graph is undefined

• A line the graph approaches but never reaches

• A point where the graph crosses the y-axis