Polynomial Behavior and Function Properties

This video serves as a midterm review guide, covering topics such as polynomials, rational functions, and trigonometry. It explains the nature of roots, end behavior, even and odd functions, and rational functions with examples. The video also discusses function manipulations, average rate of change, domain and range, optimization, exponential functions, and sinusoidal equations. Each section provides detailed explanations and examples to help students understand and apply these mathematical concepts.

What is the end behavior of an odd degree polynomial with a positive leading coefficient?

• Starts and ends at negative infinity

• Starts and ends at positive infinity

• Starts at negative infinity and ends at positive infinity

• Starts at positive infinity and ends at negative infinity

Which of the following is true for even functions?

• Not symmetrical

• Symmetrical about the origin

• Symmetrical about the y-axis

• Symmetrical about the x-axis

Where do zeros of a rational function come from?

• Neither numerator nor denominator

• Both numerator and denominator

• Denominator only

• Numerator only

What is the result of composing a function with its inverse?

• A constant function

• The inverse function

• The identity function

• The original function

How is the average rate of change of a function calculated?

• By calculating the slope between two points

• By finding the integral

• By finding the derivative

• By calculating the area under the curve

What is the domain of the function y = ln(x + 1)?

• x > 0

• x > -1

• x < 0

• x < -1

If an investment is compounded continuously, which formula is used?

• A = P(1 - rt)

• A = P(1 + rt)

• A = Pe^(rt)

• A = P(1 + r/n)^(nt)

What is the sine of 5π/6?

• 1/2

• -1/2

• √3/2

• -√3/2