Basic Functions
Functions, Powers, Multiplicty
End Behavior and Graphing
F. Theorem + Complex Zeroes
Chapter 3
100

Does x2 + 3x + 2 pass the vertical line test?

Yes

100

What are the degrees of the following functions?

Zero Function

Constant Function

Linear Function

Quadratic Function

1. Undefined

2. Zero

3. One

4. Two

100

fill in this chart

down up

up down

up up 

down down

100

Find the Rational Roots of:

f(x)=(2x+3)(2x-3)

-3/2, 3/2

100

What is the basic equation for exponential functions and what do the variables stand for?

f(x)=abx

a= initial value

b= the base

200

Which discontinuity is this?

Jump Discontinuity

200

What is Standard Form? What is Vertex Form?

y=ax2+bx+c / y=a(x-h)2+k

200

f(x)=x2-4

How many extrema does this function have?


1 extrema

200

What is the degree in number of zeroes for:

f(x)=x3-2x2+5x

degree 3 zeroes 3 (real non-real)

200

Draw an exponential growth and an exponential decay graph... What is the main rule for b for both growth and decay?

Consult Game Makers for Answers

b > 1 is growth

b < is decay

300

Vertical Asymptotes occur in rational functions when ________.

When the denominator is 0.
300

Graph this function and tell us what type of variation this is: 2x-3

Refer to the Game Makers

300

f(x)=x2-4

How many zeroes does this function have?

2 zeroes

300

Where are the zeroes of the function:

 F(x)=x4+x3-2x2+4x-24

(x-2)(x+3)(x2+4)

300

Describe the transformations of the graph f(x)=2x when it is written as f(x)=-5  (2x) 

Vertical flip and then vertical stretch by 5

400

Draw the parent function of: cubic, quadratic, square root, and absolute value.

Refer to the Game Makers.

400

Graph: f(x)=(x-1)3(x+1)2

What does the graph look like at x=1?

See the Game Makers for Answer

400

What is the graph of: F(x)= 2x2+4x-6/x+1

Include Y-intercept, X-intercept, Vertical Asymptote, and Slant Asymptote

See the Game Makers for answer

400

Create a sign chart for:

x+4/(x-1)2(x+2) (>=) 0

See Game Makers for Answer
400

What is the basic formula for either a half life or doubling life exponential function?

Half Life: f(t)= a (1/2)t/p

Doubling Life: a (2)t/p

500

Using the functions we give you, find the (f o g)(x)

(f o g) (x) = x

500

F(x)=(x+2)3(x-1)2

Find:

Odd or Even degree polynomial:

is an positive or negative?

End Behavior:

X-intercepts:

Multiplicity at each X-intercept:

Y-intercepts:

Odd

Positive

down up

x=-2, x=1

m=2, m=3


y=(0,8)

500

What is the end behavior of g(x)=-4x8+4x3+4x2 in limit notation? 

See Game Makers for Answer 

500

Write a function with zeroes at: x=-3, 4, 2, -i

f(x)=(x2-x-12)(x2-4x+5)

500
What is the basic formula for a Logistic Growth and Decay Function?

f(x)= c/1 + a (bx)

or written as

f(x)= c/1 + a (ekx)

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