College Algebra 3/29

6.4 Theorems

100

What is the degree of a cubic function?

3rd degree

200

How many factors/intercepts can be found in a 3rd degree polynomial?

At most 3

300

How many turning points in a 5th degree polynomial?

At most 4

400

What are the zeroes and the multiplicity of =(x-1)(x+2)²(x-7)³

x-1 means 1 is a zero with a multiplicity of 1

x+2 means -2 is a zero with a multiplicity of 2

x-7 means 7 is a zero with a multiplicity of 3

500

Factor x³+x²-8x-12 and determine what zeroes are present, and what multiplicity they have (if any of them do)

(x+2)²(x-3) or zeroes are -2 and 3, -2 having a multiplicity of 2.

7.1 Graphs and Behaviors

100

is 5^x increasing or decreasing?

increasing

200

is 1/2^x-4 increasing or decreasing?

decreasing

300

is 6 1/2^x  increasing or decreasing?

increasing

400

If a exponential function is increasing, what is it's behavior as x approaches infinity?

f(x) will also approach infinity

500

If an exponential function is decreasing, what will be it's behavior as x approaches infinity?

f(x) will approach 0

7.1 Exponential Functions

100

Solve 3^x=27

x=3

200

Solve 5^1-x=25

x = -1

300

Solve 6^2x=6^1-3x

x = 1/5

400

Solve 35^x+6=9^2x+8

x=10

500

Solve 25^x-125=0

x=2