Math 3 Unit 3 Flashcard 1 Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, f(x) = 2x^3 - 4x^2 + 3x - 5 is a polynomial.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 4x^5 - 3x^2 + 2, the degree is 5.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line x = a where the function approaches infinity or negative infinity as x approaches a.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find horizontal asymptotes for rational functions?

Back

For rational functions, compare the degrees of the numerator and denominator: If the degree of the numerator is less than the degree of the denominator, y = 0 is the horizontal asymptote. If they are equal, divide the leading coefficients.

Tags

CCSS.HSF-IF.C.7D

Front

What does it mean for a function to be even?

Back

A function f(x) is even if f(-x) = f(x) for all x in the domain. Its graph is symmetric about the y-axis.

Tags

CCSS.HSF.BF.B.3

Front

What does it mean for a function to be odd?

Back

A function f(x) is odd if f(-x) = -f(x) for all x in the domain. Its graph is symmetric about the origin.

Tags

CCSS.HSF.BF.B.3

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient of a polynomial determines the end behavior of the graph. If it is positive, the graph rises to the right; if negative, it falls to the right.

Front

What is the difference between a polynomial and a rational function?

Back

A polynomial is a sum of terms with non-negative integer exponents, while a rational function is a ratio of two polynomials.

Tags

CCSS.8.F.A.3

Front

What is the factor theorem?

Back

The factor theorem states that if f(c) = 0 for a polynomial f(x), then (x - c) is a factor of f(x).

Tags

CCSS.HSA.APR.B.2