Key Features of Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What determines the degree of a polynomial?

Back

The degree of a polynomial is determined by the highest power of the variable in the expression.

Front

What does the leading coefficient of a polynomial indicate?

Back

The leading coefficient is the coefficient of the term with the highest degree, and it affects the end behavior of the polynomial's graph.

Front

What is the difference between absolute max and relative max?

Back

Absolute max is the highest point over the entire graph, while relative max is the highest point in a specific interval.

Front

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

Back

The end behavior can be identified by the leading coefficient and the degree of the polynomial.

Front

What does it mean if a polynomial has an odd degree?

Back

If a polynomial has an odd degree, its graph will have opposite end behaviors; one end will go to positive infinity and the other to negative infinity.

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.

Front

What is a relative minimum in a polynomial graph?

Back

A relative minimum is a point on the graph where the function value is lower than all nearby points.

Front

How do you find the x-intercepts of a polynomial function?

Back

The x-intercepts can be found by setting the polynomial equal to zero and solving for the variable.

Front

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

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the polynomial at x=0.