Polynomial and Rational Functions

Explain a real-life scenario where a polynomial function can be used to model a situation.

• Agriculture - Predicting crop yields

• Astronomy - Calculating planetary orbits

• Medicine - Determining patient diagnosis

• Finance - Predicting stock prices

Solve the following application problem using polynomial functions: A rectangular garden has a length of 10 meters and a width of 5 meters. Find the area of the garden.

• 40 square meters

• 25 square meters

• 15 square meters

• 50 square meters

What is the degree of the polynomial function f(x) = 3x^4 - 2x^2 + 5x - 1?

• 2

• 5

• 3

• 4

How can you determine the end behavior of a polynomial function?

• Look at the y-intercept of the polynomial function.

• Look at the degree and leading coefficient of the polynomial function.

• Check the symmetry of the polynomial function.

• Count the number of terms in the polynomial function.

Using the concept of synthetic division, divide the polynomial f(x) = 2x^3 + 5x^2 - 3x + 1 by x - 2.

• Quotient: 2x^2 + 9x + 15

• Quotient: x^2 + 3x + 5

• Quotient: 3x^2 + 7x + 10

• Quotient: 4x^2 + 11x + 20

Explain the concept of a rational function and provide an example.

• An example of a rational function is f(x) = (3x^2 + 2x - 1) / (x^2 - 4).

• f(x) = (x^2 - 1) / (x - 1)

• f(x) = (4x^3 + 2) / (x^2 + 1)

• f(x) = (x^2 + 3) / (2x - 5)

Solve the rational function: (3x^2 + 2x - 8) / (x - 2).

• 3x + 4

• 4x - 3

• x + 2

• 2x + 3

What is the vertical asymptote of the rational function f(x) = (x^2 - 4) / (x + 2)?

• x = -2

• x = 0

• x = 4

• x = -4

Discuss the behavior of a rational function near its vertical asymptote.

• The function remains constant near the asymptote

• The function oscillates near the asymptote

• The behavior near a vertical asymptote of a rational function involves approaching positive or negative infinity.

• The function approaches a finite value near the asymptote

How can you determine the domain of a rational function?

• Identify values that make the denominator zero and exclude them from the domain.

• Select values that make the numerator zero

• Include all real numbers in the domain

• Only consider positive values for the domain