Polynomials test rev activty

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 + 7 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 f(x) = 3x^4 - 2x^2 + 5, the degree is 4.

Front

What does the leading coefficient of a polynomial indicate?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It affects the end behavior of the polynomial function.

Front

Describe the end behavior of a polynomial function with an even degree and a positive leading coefficient.

Back

The end behavior will rise on both ends; as x approaches positive or negative infinity, f(x) approaches positive infinity.

Front

Describe the end behavior of a polynomial function with an odd degree and a positive leading coefficient.

Back

The end behavior will fall on the left and rise on the right; as x approaches negative infinity, f(x) approaches negative infinity, and as x approaches positive infinity, f(x) approaches positive infinity.

Front

What is a y-intercept of a polynomial function?

Back

The y-intercept is the point where the graph of the polynomial crosses the y-axis, which occurs when x = 0.

Front

How do you find the y-intercept of the polynomial f(x) = -3x^4 + x^3 - 2x^2 + x - 1?

Back

To find the y-intercept, substitute x = 0 into the polynomial: f(0) = -1. Thus, the y-intercept is -1.

Front

What is an odd function?

Back

An odd function is a function that satisfies the property f(-x) = -f(x) for all x in its domain. Its graph is symmetric about the origin.

Front

What is an even function?

Back

An even function is a function that satisfies the property f(-x) = f(x) for all x in its domain. Its graph is symmetric about the y-axis.

Front

What is the significance of the end behavior of a polynomial?

Back

The end behavior of a polynomial helps to determine how the graph behaves as x approaches positive or negative infinity, which is crucial for sketching the graph.