Question

Given the parent function of f(x) = x4, what change will occur when the function is changed to -f(2x)?
@jim_thompson5910

Answer 1

graph y = x^4 using desmos

Answer 2

then add on -x^4 for the second row

and finally, add on -(2x)^4 for the third row

Answer 3

hopefully you see how the graph is changing

Answer 4

Oh okay thank you so much. I'll let you check my answer later

Answer 5

alright

Answer 6

Graph opens the opposite way and is narrower?

Answer 7

@jim_thompson5910

Answer 8

very good

Answer 9

thanks!

Answer 10

What is the end behavior of the function f(x) = -x3 + 2x2 + 4x + 5?

Up on the left, up on the right
Up on the left, down on the right <----- MY ANSWER
Down on the left, up on the right
Down on the left, down on the right

Is it right? @jim_thompson5910

Answer 11

correct

Answer 12

What are the coordinates of the turning point for the function f(x) = (x + 3)3 + 1?
How would I do this one? @jim_thompson5910

Answer 13

the turning point of y = x^3 is (0,0)

graph both y = x^3 and y = (x+3)^3 + 1 in desmos and notice how the shifts occur

Answer 14

hopefully you see the turning point?

Answer 15

in different rows right? @jim_thompson5910

Answer 16

yes each row is a separate equation/graph

Answer 17

it says the turning point for x^3 is (0, 0) then for (x+3)^3 it changes to (-3, 0) but that isn't any of my answer choices.

Answer 18

@jim_thompson5910

Answer 19

now shift things up 1 unit

Answer 20

you forgot about the +1 at the end

Answer 21

ohhh so (-3, 1)?

Answer 22

@jim_thompson5910

Answer 23

you nailed it

Answer 24

Thank you!! I'll keep doing this but I'll definitely need your help, so it would be great if you just keep an eye out for my questions and help me out if you don't mind :)

Answer 25

What polynomial identity should be used to prove that 133 = 125 + 8?

Difference of Cubes
Difference of Squares
Square of Binomial
Sum of Cubes <----- MY ANSWER
@jim_thompson5910

Answer 26

@jim_thompson5910 is that right?

Answer 27

yes because 125 = 5^3 and 8 = 2^3

125 + 8 = 5^3 = 2^3 = sum of cubes

Answer 28

yep! :D

Answer 29

Use the graph of the function f(x) = x3 - 3x2 - x + 3 to answer this question:

graph of x cubed minus 3 x squared minus x plus 3

What is the average rate of change from x = -1 to x = 2?

-3
-1 <----- MY ANSWER
0
3
What about this one?

Answer 30

it is correct

Answer 31

Another one i can't seem to figure out it's very confusing @jim_thompson5910

Answer 32

Select the graph and the description of the end behavior of f(x) = -x3 - 2.

graph that decreases from left to right that passes through ordered pairs negative 2, 10; negative 1, 3; 0, 2; 1, 1; and 2, negative 6
This is a cubic function. The end behavior of the graph will decrease to the right and increase to the left.
graph that increases from left to right that passes through ordered pairs negative 2, negative 6; negative 1, 1; 0, 2; 1, 3; and 2, 10
This is a cubic function. The end behavior of the graph will increase to the right and decrease to the left.
graph that increases from left to right that passes through ordered pairs negative 2, negative 10; negative 1, negative 3; 0, negative 2; 1, negative 1; and 2, 6
This is a cubic function. The end behavior of the graph will increase to the right and decrease to the left.
graph that decreases from left to right that passes through ordered pairs negative 2, 6; negative 1, negative 1; 0, negative 2; 1, negative 3; and 2, negative 10
This is a cubic function. The end behavior of the graph will decrease to the right and increase to the left.

Answer 33

yikes...giant wall of text lol

Answer 34

LOL sorry I'll try to graph them if u would like?

Answer 35

it's fine lol, but graphing -x^3 - 2 should help you find the answer

Answer 36

oh okay let me try that out

Answer 37

to find ordered pairs on the graph, you can also set up a table

Answer 38

I got D as the answer @jim_thompson5910

Answer 39

how many answer choices are there?

Answer 40

A through D

Answer 41

ok

Answer 42

choice D says


graph that decreases from left to right that passes through ordered pairs negative 2, 6; negative 1, negative 1; 0, negative 2; 1, negative 3; and 2, negative 10

This is a cubic function. The end behavior of the graph will decrease to the right and increase to the left.



right?

Answer 43

not sure where it starts

Answer 44

yeah ur right but I graphed it on desmos and it looked the same as my answer choice @jim_thompson5910

Answer 45

ok let me graph real quick

Answer 46

ok

Answer 47

yeah it decreases and it goes through (0,-2)

Answer 48

alright! another one lol I am extremely sorry

Answer 49

What are the possible numbers of positive, negative, and complex zeros of f(x) = -3x4 + 5x3 - x2 + 8x + 4?

Positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
Positive: 1; negative: 3 or 1; complex: 2 or 0
Positive: 3 or 1; negative: 1; complex: 2 or 0
Positive: 4 or 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0

Answer 50

@jim_thompson5910

Answer 51

is it B? @jim_thompson5910

Answer 52

how many sign changes are there in -3x^4+5x^3-x^2+8x+4

Answer 53

2

Answer 54

I count 3 sign changes


from -3x^4 to +5x^3
from +5x^3 to -x^2
from -x^2 to +8x

Answer 55

oh yeah sorry my bad lol ur right

Answer 56

so there are at most 3 positive real roots

Answer 57

now we need to find f(-x)

f(x) = -3x^4+5x^3-x^2+8x+4

f(-x) = -3(-x)^4+5(-x)^3-(-x)^2+8(-x)+4

f(-x) = -3x^4-5x^3-x^2-8x+4


how many sign changes are there in f(-x) ?

Answer 58

2? @jim_thompson5910

Answer 59

just one this time: -8x to +4

Answer 60

so there is at most 1 negative real root

Answer 61

now let's say we had 3 positive real roots

that leaves 1 root left over, so we'd have 1 negative real root because complex roots always come in pairs

Answer 62

if we had 2 positive real roots, then we'd have 2 complex roots as well

Answer 63

one sec, reading something on the descartes rule of signs

Answer 64

okayy

Answer 65

ok according to this

http://www.purplemath.com/modules/drofsign.htm

we subtract by 2

Answer 66

so we'll have 3 or 1 positive root

Answer 67

Thanks @jim_thompson5910

Answer 68

Use the graph of the function f(x) = 3x4 - x3 + 3x2 + x - 3 to answer this question:

graph of 3 x to the fourth, minus x cubed, plus 3 x squared, plus x minus 3

What is the average rate of change from x = -1 to x = 0?

-6
-3
3
6
I'm stuck on this.. @jim_thompson5910

Answer 69

you need to evaluate

\[\Large \frac{f(-1)-f(0)}{-1-0}\]

Answer 70

idk what to do @jim_thompson5910

Answer 71

Can u tell me what to do? @jim_thompson5910

Answer 72

do you know what f(-1) means or represents?

Answer 73

y?

Answer 74

is the answer 3? @jim_thompson5910

Answer 75

f(-1) is the y value when x = -1

Answer 76

to find f(-1) you plug x = -1 into the function f(x) and evaluate

Answer 77

what is f(-1) equal to?

Answer 78

I got 3

Answer 79

@jim_thompson5910

Answer 80

f(0) = ???

Answer 81

i thought u said f(-1)??

Answer 82

yes sorry, I want to know both f(-1) and f(0)

f(-1) = 3 is correct

now what is f(0) equal to

Answer 83

0?

Answer 84

nope

Answer 85

plug x = 0 into the function and evaluate

Answer 86

i did and i got 0 somehow

Answer 87

try it again, you should get -3

Answer 88

-3 isn't the answer btw, it's just the value of f(0)

Answer 89

oh yeah i got -3 sorry for 3*0^2 I somehow got 3 instead of 0 i wasnt thinking lol

Answer 90

I see

Answer 91

f(-1) = 3
f(0) = -3
\[\Large \frac{f(-1)-f(0)}{-1-0} = \frac{3-(-3)}{-1-0} = ???\]

Answer 92

-6

Answer 93

@jim_thompson5910

Answer 94

-6 is the ultimate answer

Answer 95

correct

Answer 96

Thank you sooo much!!! how can u make something seem SOOO easy seriously u make me feel dumb all the time LOL @jim_thompson5910