Precalc. BC Semester 1 Exam Practice

Front

What is the factor theorem in polynomial functions?

Back

The factor theorem states that if a polynomial f(x) has a factor (x - c), then f(c) = 0. This means that c is a root (or zero) of the polynomial.

Front

How do you find the complex zeros of a polynomial?

Back

To find the complex zeros of a polynomial, first factor the polynomial if possible, then use the quadratic formula or synthetic division to find the roots, including complex ones.

Front

What is the average rate of change of a function?

Back

The average rate of change of a function f(x) over an interval [a, b] is given by the formula: \( \frac{f(b) - f(a)}{b - a} \).

Front

What is the significance of the leading coefficient in a polynomial function?

Back

The leading coefficient determines the end behavior of the polynomial function. If it is positive, the function rises to the right; if negative, it falls to the right.

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What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements. This means that for every y in the range, there is exactly one x in the domain.

Front

How do you determine the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined. It can be found by identifying restrictions such as division by zero or square roots of negative numbers.

Front

What is the process for finding the inverse of a function?

Back

To find the inverse of a function f(x), swap the x and y in the equation and solve for y. The resulting equation is the inverse function, denoted as f^(-1)(x).

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form \( f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 \), where a_n, a_{n-1}, ..., a_0 are constants and n is a non-negative integer.

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What is synthetic division and when is it used?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor of the form (x - c). It is faster and requires less writing.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation \( ax^2 + bx + c = 0 \) and is given by: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).