Polynomial Functions, radical, probability review

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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, where n is a non-negative integer.

Front

What are the roots of a polynomial?

Back

The roots of a polynomial are the values of x for which the polynomial equals zero. They are also known as the solutions or zeros of the polynomial.

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How do you determine if x - r is a factor of a polynomial f(x)?

Back

Use the Remainder Theorem: If f(r) = 0, then x - r is a factor of f(x).

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What is the Remainder Theorem?

Back

The Remainder Theorem states that when a polynomial f(x) is divided by x - r, the remainder of this division is f(r).

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What does it mean for a polynomial to have a minimum or maximum?

Back

A polynomial has a minimum at a point if the value of the polynomial at that point is less than the values at nearby points. It has a maximum if the value is greater than the values at nearby points.

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What is a transformation of a function?

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A transformation of a function refers to changes made to the function's graph, such as shifts, stretches, compressions, or reflections.

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What does it mean to reflect a function over the x-axis?

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Reflecting a function over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

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What is the significance of zeros in a polynomial function?

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Zeros of a polynomial function are the x-values where the function intersects the x-axis. They indicate the roots of the polynomial.

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How do you find the zeros of a polynomial function?

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To find the zeros of a polynomial function, set the polynomial equal to zero and solve for x.