AP Precalculus: Polynomial and Rational Functions flashcards

Question 1

What is the term for a vertical line through the vertex of a parabola, about which the parabola is symmetric?

Accepted Answer

Axis of symmetry (x = -b/(2a) for a quadratic in general form)

Question 2

What is the formula for the axis of symmetry of f(x) = ax² + bx + c?

Accepted Answer

x = -b/(2a)

Question 3

What is the complex conjugate of a complex number?

Accepted Answer

The complex number with the sign of the imaginary part changed and the same real part

Question 4

What is the name of a coordinate system whose horizontal axis shows the real part and vertical axis shows the imaginary part of a complex number?

Accepted Answer

The complex plane

Question 5

What is a function called whose graph can be drawn without lifting the pen, because it has no breaks?

Accepted Answer

A continuous function

Question 6

What is the degree of a polynomial?

Accepted Answer

The highest power of the variable that occurs in it

Question 7

What rule gives the maximum possible number of positive and negative real zeros of a polynomial from the sign changes of f(x) and f(-x)?

Accepted Answer

Descartes' Rule of Signs

Question 8

What is the term for a relationship in which one variable is a constant multiple of the other?

Accepted Answer

Direct variation

Question 9

What is the description of how a function's graph behaves as the input decreases without bound and increases without bound?

Accepted Answer

End behavior

Question 10

What does the Factor Theorem say about k being a zero of f(x)?

Accepted Answer

k is a zero of f(x) if and only if (x - k) is a factor of f(x)

Question 11

What theorem states that a polynomial function of degree greater than 0 has at least one complex zero?

Accepted Answer

The Fundamental Theorem of Algebra

Question 12

What is a horizontal line y = b called that the graph approaches as the inputs increase or decrease without bound?

Accepted Answer

A horizontal asymptote

Question 13

What is a vertical line x = a called that the graph tends toward positive or negative infinity near, as the inputs approach a?

Accepted Answer

A vertical asymptote

Question 14

What is a number of the form bi, where i = √(-1), called?

Accepted Answer

An imaginary number

Question 15

What relationship between two variables has a constant product?

Accepted Answer

Inverse variation

Question 16

What is a function called that has an inverse function?

Accepted Answer

An invertible function

Question 17

What is the coefficient of the leading term of a polynomial called?

Accepted Answer

The leading coefficient

Question 18

What is the term with the highest power of the variable in a polynomial called?

Accepted Answer

The leading term

Question 19

According to the Linear Factorization Theorem, how many linear factors does a polynomial have, counting multiplicity, and what form do they take?

Accepted Answer

As many as its degree, each of the form (x - c) with c a complex number

Question 20

What is the number of times a given factor appears in the factored form of a polynomial called?

Accepted Answer

The multiplicity of that factor

Question 21

What kind of function has the form f(x) = kx^p, with k and p constants?

Accepted Answer

A power function

Question 22

What is a function that can be written as the ratio of two polynomials called?

Accepted Answer

A rational function

Question 23

What does the Remainder Theorem say about dividing f(x) by x - k?

Accepted Answer

The remainder equals f(k)

Question 24

What is a single point where a function is undefined, but which would make the function continuous if filled in (appearing as a hole), called?

Accepted Answer

A removable discontinuity

Question 25

What is the name of a shortcut method for dividing a polynomial by a binomial of the form x - k?

Accepted Answer

Synthetic division

Question 26

What is the location on a graph where the function changes direction called?

Accepted Answer

A turning point

Question 27

What is the point where a parabola changes direction, corresponding to its minimum or maximum value, called?

Accepted Answer

The vertex

Question 28

What are the values of x at which a function's output y is 0 called?

Accepted Answer

The zeros (also called roots)

Question 29

What is a relationship called in which one quantity equals a constant divided by the other?

Accepted Answer

Inversely proportional (varies inversely)

Question 30

What does 'y varies directly with x' mean?

Accepted Answer

y is a constant multiple of x

Question 31

What is the value of i²?

Accepted Answer

-1

Question 32

A polynomial of degree n has at most how many turning points?

Accepted Answer

n - 1

AP Precalculus: Polynomial and Rational Functions flashcards

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