Precalculus: Polynomial and Rational Functions flashcards

Question 1

What is an imaginary number?

Accepted Answer

A number of the form bi, where i = sqrt(-1)

Question 2

What is the complex conjugate of a complex number?

Accepted Answer

The number with the same real part and the sign of the imaginary part reversed

Question 3

In the complex plane, which axis shows the imaginary part?

Accepted Answer

The vertical axis (the horizontal axis shows the real part)

Question 4

How often do the powers of i repeat?

Accepted Answer

Every four powers; they are cyclic

Question 5

What is the general form of a quadratic function?

Accepted Answer

f(x) = ax^2 + bx + c, with a, b, c real and a ≠ 0

Question 6

What is the standard (vertex) form of a quadratic function?

Accepted Answer

f(x) = a(x - h)^2 + k; the vertex is (h, k)

Question 7

What equation gives the axis of symmetry of the parabola y = ax^2 + bx + c?

Accepted Answer

x = -b/(2a)

Question 8

What is the quadratic formula?

Accepted Answer

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Question 9

What gives the maximum or minimum value of a quadratic function?

Accepted Answer

The y-value of the vertex

Question 10

What is the degree of a polynomial?

Accepted Answer

The highest power of the variable that appears in it

Question 11

What is the leading coefficient of a polynomial?

Accepted Answer

The coefficient of the term with the highest power of the variable

Question 12

At most how many turning points does a polynomial of degree n have?

Accepted Answer

n - 1

Question 13

At most how many x-intercepts does a polynomial of degree n have?

Accepted Answer

n

Question 14

At a zero of odd multiplicity, what does a polynomial's graph do?

Accepted Answer

It crosses the horizontal axis

Question 15

At a zero of even multiplicity, what does a polynomial's graph do?

Accepted Answer

It touches the horizontal axis

Question 16

If f(a) and f(b) differ in sign, what does the Intermediate Value Theorem guarantee?

Accepted Answer

At least one c between a and b has f(c) = 0

Question 17

What does the Remainder Theorem state?

Accepted Answer

Dividing a polynomial f(x) by x - k leaves remainder f(k)

Question 18

What does the Factor Theorem state?

Accepted Answer

k is a zero of f(x) exactly when f(x) has (x - k) as a factor

Question 19

What does the Rational Zero Theorem say about possible rational zeros p/q?

Accepted Answer

p divides the constant term and q divides the leading coefficient

Question 20

What does the Fundamental Theorem of Algebra state?

Accepted Answer

Any polynomial function whose degree exceeds 0 has one or more complex zeros

Question 21

What does Descartes' Rule of Signs determine?

Accepted Answer

The greatest possible counts of positive and of negative real zeros, using sign changes in f(x) and f(-x)

Question 22

What is a rational function?

Accepted Answer

A function expressible as one polynomial divided by another

Question 23

What is a removable discontinuity?

Accepted Answer

A single point where a function is undefined that would make it continuous if filled in; it shows as a hole in the graph

Precalculus: Polynomial and Rational Functions flashcards

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