Understanding 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 characteristics, and transformations. The video also discusses rational functions, asymptotes, and how to find zeros and holes. Techniques like polynomial long division and the binomial theorem are introduced. The video emphasizes understanding function models through context clues and calculator use.

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

• Exponential and Logarithmic

• Trigonometric and Hyperbolic

• Linear and Quadratic

• Polynomial and Rational

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

• Range

• Domain

• Slope

• Intercept

How is the rate of change of a function graphically represented?

• Vertex

• Axis

• Intercept

• Slope

What is the rate of change in a linear function over any interval?

• Variable

• Constant

• Undefined

• Zero

Which of the following is NOT a type of polynomial function?

• Exponential

• Quadratic

• Cubic

• Linear

What does an even degree in a polynomial function indicate about its graph?

• It is always decreasing

• It is always increasing

• It has a global maximum or minimum

• It has no zeros

What is the term for the behavior of a graph as it extends to the left or right?

• Vertex

• End Behavior

• Slope

• Intercept

What are rational functions composed of?

• Two polynomials

• Two logarithms

• Two exponential functions

• Two trigonometric functions

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

• Set the entire function to zero

• Set the denominator to zero

• Set both numerator and denominator to zero

• Set the numerator to zero

What is a vertical asymptote in a rational function?

• A line the graph approaches but never touches

• A point where the graph crosses the y-axis

• A line the graph intersects

• A point where the graph crosses the x-axis