Math is Fun

End Behavior

100

What does an odd degree of a polynomial determine about the end behavior?

The ends go in opposite directions.

200

What is the end behavior for the function:

f(x)=4x⁵-3x²+8?

x->-infinity

f(x)->infinity

300

At which y value does x go to infinity & -infinity for the function: f(x)=3x²-5x+2 ?

y=3

400

For the function f(x)=-2x⁴+5x³-7x+1

as x approaches -infinity

f(x) approaches ???

-infinity

500

Find the slant asymptote of 

f(x)=(2x³-5x²+1)

--------------------

(x²-4)

y=2x-5

Rational Functions

100

What shape is formed by the end behavior of an even and positive function?

Concave up/ U shape

200

Identify zeros and VA

(x+3)(x+5)

------------

(x+1)(x+9)

VA: [-1,-9]

Zeros: [-3,-5]

300

Identify the zeros and VA

(x+3)(x+4)

-------------

(x+2)(x+1)

[-2,-1]

400

Identify the zeros and VA

(x-3)(x+1)

------------

(x-3)(x-3)

None

500

Find the H.A

x²+3x-18

-----------

x³+4x²+7x

H.A=0

Zeros

100

What is another name for the zeros of a function?

x-intercept

200

Identify the zeros

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

x=-2 x=1 x=3

300

Identify the zeros

(x+2)(x-10)

-------------

(x-10)(x+3)

x=-2

400

Identify the zeros

(x+7)(x-5)

-----------

(x-8)(x-5)

x=-7

500

Find the zeros

x²+2x-8

----------

(x+7)(x-1)

x=2

x=-4

Asymptotes

100

What is determined by the values left in the denominator of a rational function?

Vertical Asymptote

200

Find the H.A

(x-3)(x+2)²

-------------

(x-2)(x+7)

None

300

Find the V.A

(x+2)(x-5)

------------

(x-5)(x-5)

x=5

400

Find the H.A

(x-3)(x+4)

------------

(x-2)(x+6)²

H.A=0

500

Find the V.A

x²+3x-18

----------

x²-3x-18

x=6

x=-3

Holes

100

What part of a function is determined by what cancels out in both the numerator and the denominator?

Hole

200

Where is the hole in

(x-10)(x+3)

(x-10)(x+7)

x=10

300

Identify the holes

x²+2x-8

---------

(x-2)(x+17)

x=2

400

Identify the hole

x²+3x-18

----------

(x-3)(x+8)

x=3

500

Identify the holes

x²-3x-18

----------

(x-6)(x-3)

x=6