College Algebra Major Review 2

End Behavior

100

Describe the end behavior of this graph

2x⁴+9x³-2x²-4x 

rises to the right and rises to the left

200

describe the end behavior

-4x⁵+8x⁴-5x²-7

rises to the left and falls to the right

300

describe the end behavior

5x(2x-5)²

falls to the left and rises to the right

400

Describe the end behavior

-2x⁴+3x³-2x+1

falls to the left and falls to the right

500

Describe the end behavior 

3x-4x⁵-2x³+14x²

rises to the left and falls to the right

Characteristics of a function

100

15v³-9+3v²-v

find the degree and coefficiant

degree: 3

Coefficiant:15

200

List each zero according the the multiplicity.

(x+11)(x+3)(x-11)²(x-12)

zeroes of multiplicity 1: -11,-3,12

zeroes of multiplicity 2: 11

zeroes of multiplicity 3: none

300

f(x) = x²+10x+28

does the function have a min or max?

where does it occur?

a minimum

(-5,3)

400

for g(x) = x²+3 and h(x) = x-4 find g(h(x)) and its domain.

g(h(x)) = (x-4)²+3

domain: (-infinity, infinity)

500

u(x) = -5x-3        w(x) = -2x+1

find u(w(-1)) and w(u(-1)).

u(w(-1)) = -18

w(u(-1)) = -3

Functions

100

Go to slide [6]

(-infinity,infinity) -> 0 at -4, x can't be -4

(-infinity,-8)U(-8,1)U(1,infinity)

200

Go to slide [7]

[-4,infinity)

300

Go to slide [8]

[6,9)U(9,infinity)

400

Go to slide [9]

6

500

go to slide [10]

3x²+x+6

3x³+18x²

-18

Graphs

100

How would you apply the transformations of this graph

[slide 11]

answer on slide

200

Identify the functions of the graph [slide 12]

answer on slides

300

Write the new function for the graph slide [13]

(x+4)^1/2-3

400

Describe the characteristics of this function. [14]

on slide

500

Describe the characcteristics of this function [14]

on slide

Misc

100

Slide [16]

slide [16]

200

slide 17

slide 17

300

slide [18]

g(-1) = 1

g(2) = 4

g(4) = 4

400

A ball is thrown from a height of 70 feet with an initial downward velocity of 4 ft/s. The ball's height h (in feet) after t seconds is given by the following.

h= 70-4t-16t²

How long after the ball is thrown does it hit the ground? 

1.97 seconds

500

A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function:

C(x) = x²-240x+24,532

What is the minimum unit cost? 

$10,132