Polynomial Functions!

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression that involves 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, where a_n ≠ 0.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) > f(x2).

Front

What is an x-intercept?

Back

An x-intercept is a point where the graph of a function crosses the x-axis. At this point, the value of the function is zero.

Front

What is an absolute maximum?

Back

An absolute maximum is the highest point over the entire domain of a function. It is the largest value that the function attains.

Front

What is an absolute minimum?

Back

An absolute minimum is the lowest point over the entire domain of a function. It is the smallest value that the function attains.

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.

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.

Front

What is the end behavior of a polynomial function?

Back

The end behavior describes how the values of the function behave as x approaches positive or negative infinity.

Front

What is a turning point in a polynomial function?

Back

A turning point is a point where the function changes direction from increasing to decreasing or vice versa.