Mathematics Exam Review

Flashcards created to help review key concepts for the mathematics exam.

To rationalize an expression with radicals, you should multiply by __.

The conjugate of the expression.

When simplifying expressions using properties of exponents, remember that negative exponents represent __.

The reciprocal of the base raised to the positive exponent.

Operations with complex numbers involve and .

Addition, subtraction, multiplication, and division.

To solve a literal equation for a given variable, you need to isolate the __.

Variable of interest.

One method to solve a quadratic equation is by using the __.

Quadratic formula.

Two lines are if they have the same slope and if the product of their slopes is -1.

Parallel; Perpendicular.

End behavior in limit notation describes the behavior of polynomial functions as __ approaches infinity.

x.

To write a polynomial function given the zeros and multiplicity, you use the format __.

f(x) = a(x - r1)^(m1)(x - r2)^(m2)…

Horizontal and vertical asymptotes of rational functions can be found by analyzing __.

The degrees of the polynomial in the numerator and denominator.

Operations with polynomials include and .

Addition, subtraction, multiplication, and division.

To solve rational equations, it's important to find a common __.

Denominator.

Simplifying radicals involves both and .

Numbers; variables.

To find the inverse of a function, you switch the and .

x; y.

To determine the factors of a polynomial, you can use methods such as or .

Factoring; synthetic division.

Evaluating a piecewise function involves identifying which __ applies to the input.

Condition.

Partial fraction decomposition is used to break down __ into simpler fractions.

Rational expressions.

Finding the zeros of a polynomial function is equivalent to solving __.

The equation f(x) = 0.

To solve a rational inequality, you need to consider the zeros and __ of the expressions involved.

Asymptotes.

The domain of a function consists of all __ over which the function is defined.

Possible input values.