Polynomial Graphs Review

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.

Front

How do you find the zeros of a polynomial function?

Back

The zeros of a polynomial function are the values of x for which the function equals zero. They can be found by factoring the polynomial or using the quadratic formula for quadratic functions.

Front

What are increasing intervals in a polynomial graph?

Back

Increasing intervals are the ranges of x-values where the polynomial function is rising as x increases. This can be determined by analyzing the first derivative of the function.

Front

What are decreasing intervals in a polynomial graph?

Back

Decreasing intervals are the ranges of x-values where the polynomial function is falling as x increases. This can be determined by analyzing the first derivative of the function.

Front

What is the range of a polynomial function?

Back

The range of a polynomial function is the set of all possible output values (y-values) that the function can produce. It can be determined by analyzing the function's behavior and critical points.

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression. It determines the polynomial's end behavior and the maximum number of zeros.

Front

What is the leading coefficient of a polynomial?

Back

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

Front

How do you determine the multiplicity of a zero?

Back

The multiplicity of a zero refers to the number of times a particular zero appears as a root of the polynomial. It can be determined from the factors of the polynomial.

Front

What is the significance of the y-intercept in a polynomial graph?

Back

The y-intercept of a polynomial graph is the point where the graph crosses the y-axis. It can be found by evaluating the polynomial at x = 0.