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Flashcards in 1EXAM- HPreCalc Deck (335)
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is (x-1)(x^2+x+1) a product of linear factors

no, simplify the last trinomial by doing quadratic formula to get a product of linear factors

1

3 key numbers means

4 test regions

2

do you put brackets around solutions that make the bottom 0

no

3

is x^2 + 49 factorable?

yes
(x-7i) (x+7i)

4

The theorem that can be used to determine the possible numbers of positive real zeros and negative real zeros of a function is called __________ __________ of ________

Descartes's Rule, Signs

5

the formula that relates cost, revenue, and profit is ______

profit=revenue-cost

6

key numbers are ____

whatever makes the top and bottom 0

7

how do you find HA if the numerator's degree=denominator's degree

y=ratio of leading coefficients
f(x)=2x-5/4-x HA:y=-2

8

The _______ ________ _______ states that if f(x) is a polynomial of degree n (n>0), then f(x) has precisely n linear factors

linear factorization theorem

9

what is intermediate form? is it the same as undefined

0/0, no

10

The _______ _______ of _______ states that if f(x) is a polynomial of degree n (n>0), then f has at least one zero in the complex number system

fundamental, theorem, algebra

11

All graphs _____ the asymptotes

Follow

12

Increasing and decreasing intervals use the ___ values

X (watch asymptotes)

13

what is upper bound

you plug in a higher number and get all positive sums in return
this will be your highest zero

14

Make sure graphs don't cross if there aren't enough X intercepts

..

15

When finding key points of rational functions ___ first

Simplify

16

how do you find the vertical asymptote

whatever makes the denominator 0
roots of denominator
x=
be sure to factor function first as asymptotes might cancel

17

for the rational function f(x)=N(x)/D(x), if the degree of N(x) is exactly one more than the degree of D(x), then the graph of f has a ______ (or oblique) ________

slant asymptote

18

how do you factor a perfect cube

in the first (), take the cubed root of both variables in the equation
in the second (), first, put in whatever you need to get the leading coefficient, then put in the opposite of the product of the first (), then whatever you need to get the constant

19

slant asymptotes and parabolic asymptotes all begin with

y=
so do HA
VA begins with x=

20

If a+bi is a complex zero of a polynomial with real coefficients, then so is its ________, a-bi

conjugate

21

write x^6-x^7 as a product of linear factors

(x)(x)(x)(x)(x)(x)(1-x)

22

Why is x^4 + x^2-60 guaranteed two real roots

It's down 60 going up eternally

23

Increasing and decreasing intervals use the ___ values

X (watch asymptotes)

24

A real number b is a ______ bound for the real zeros of f when no real zeros are less than b, and is a ______ bound when no real zeros are greater than b

lower, upper

25

To solve a polynomial inequality, find the _______numbers of the polynomial, and use these numbers to create __________ ________ for the inequality

critical/key, test intervals

26

what is DesCartes's Rule of signs

the number of positive real zeros=the number of sign variations or less than that by an even integer
the number of negative real zeros=the number of sign variations at
f(-x) or less than that by an even integer

27

when f(x)--->+/- infinity as x--->a from the left or right, x=a is a _______ ________ of the graph of f

vertical asymptote

28

what does lower bound say

you plug in a negative number and get alternating sums in return,
this will be your lowest zero

29

Can an answer written as the product of linear factors have imaginary factors?

Yes, they are still linear