Question

.Use the graph below to answer the question that follows:
What are the amplitude, period, and midline of the function?

Amplitude: 8; period: π; midline: y = 1

Amplitude: 8; period: 2π; midline: y = 5

Amplitude: 4; period: 2π; midline: y = 5

Amplitude: 2; period: π; midline: y = 1

Answer 1

Pick any point on the graph, say (0,-1)

Answer 2

now trace along the graph (going from left to right) and tell me when the point you trace gets to be at the same horizontal level as (0,-1)

what is the x coordinate of this next point?

Answer 3

Pi.

Answer 4

so when we get to x = pi, the whole process repeats itself again

that means the period is pi

Answer 5

So, its either A or D ;o

Answer 6

what is the distance from the highest peak to the lowest valley (only focus on the vertical y component)

Answer 7

5?

Answer 8

the lowest it goes is y = -1

the highest it goes is y = 3

Answer 9

subtract the two

3 - (-1) = 3 + 1 = 4

Answer 10

So the total distance is 4 units

cut that in half to get the amplitude

basically the distance from center midline to peak (or center midline to valley)

Answer 11

So. 2?

Answer 12

yes

Answer 13

SO ITS D :D

Answer 14

and the midline is basically the midpoint between the peak & valley

Answer 15

Can you help me with more, PLEASEEE?

Answer 16

sure

Answer 17

Same question? or new one?

Answer 18

either way works

Answer 19

At the farmer's market, there is a scale that measures the weight of fruit and vegetables. The needle is 16 cm long and it rotated 68° when Danielle placed six oranges on it. How far did the needle travel as it rotated?

272 pi over 45

45 pi over 272

1088π

544π

Answer 20

what symbol comes after "and it rotated 68"

Answer 21

degrees?

Answer 22

its the degree sign. yeah.

Answer 23

oh ok

Answer 24

what is the circumference of this whole circle?

Answer 25

Is that 2(pi)(r)> Is the radius 4?

Answer 26

?*

Answer 27

"The needle is 16 cm long" so r = 16

Answer 28

So 2(3.14)(16)?

Answer 29

correct, which is what approximately?

Answer 30

100.48

Answer 31

that is the total distance it would travel if it traveled 360 degrees

Answer 32

however, it only does 68 degrees

so it does 68/360 of the entire circle

Answer 33

that means you multiply that fraction by the circumference to get the distance you travel just along that little arc

Answer 34

Which is like 18.9.

Answer 35

correct

Answer 36

Which answer choice would that be?

Answer 37

hmm let me think

Answer 38

it looks like they used radians

Answer 39

Yeah, i got confused.

Answer 40

so we convert 68 degrees to radians by multiplying it by pi/180

68*(pi/180) = 68pi/180 = 17pi/45

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

Now that we have the central angle in radians, we can just multiply it by the radius to get the arc length

(radius)*(angle in radians) = (16)*(17pi/45) = (16*17pi/45) = 272pi/45

Answer 41

OO. So A c:

Answer 42

the nice thing about radians is that you can use them to find arc length with that formula

however, radians are a bit harder to think about compared to degrees in my mind

Answer 43

yes A

Answer 44

You dont know how much you're helping me. xD

Answer 45

Which of the following functions has the greatest y-intercept?


f(x)

x y
−3 9
−2 4
−1 1
0 0
1 1
2 4
g(x) = 5 cos(3x) − 5

f(x)

g(x)

f(x) and g(x) have the same y-intercept

Not enough information

Answer 46

Dont mind the boxes in the first.

Answer 47

what's the y intercept of f(x)?

Answer 48

f(x)

x y
−3 9
−2 4
−1 1
0 0
1 1
2 4

Answer 49

Yeah, i dont know. :c

Answer 50

the y-intercept always occurs when x = 0

Answer 51

this is because this is when the graph crosses that vertical y axis

Answer 52

so what is the y value when x = 0?

Answer 53

0.

Answer 54

therefore, the y intercept of f(x) is 0

Answer 55

for g(x), plug in x = 0 to get ???

Answer 56

0

Answer 57

so they both have the same y intercept

Answer 58

and this happens to be at the origin

Answer 59

What are the x-coordinates for the maximum points in the function f(x) = 4 cos(2x − π) from x = 0 to x = 2π?

x = 3 pi over 2, x = π

x = pi over 2, x = 3 pi over 2

x = 0, x = 2π

x = 0, x = π

Answer 60

Where the question marks are, are pi signs.

Answer 61

is this a calculus class?

Answer 62

Nu, Trig xD

Answer 63

ok, we'll have to rely on the calculator then

Answer 64

what kind of calculator do you have?

Answer 65

My mom has mine >.<

Answer 66

But it was a Ti-84.

Answer 67

so you currently don't have one?

Answer 68

Nope, i have my ipod.

Answer 69

and can you draw out the function? I see a lot of boxes where symbols are supposed to go

Answer 70

its like my browser can't display them

Answer 71

Mine cant either. and okay. \[f(x)=4\cos(2x-\Pi) from x=0 \to x=2\Pi \]

Answer 72

thanks

Answer 73

The question marks are just pi signs xD

Answer 74

If we were to graph that function, we would get this

http://www.wolframalpha.com/input/?i=4*cos%282x-pi%29

Answer 75

hmm that got cut off, let me find another graph program

Answer 76

Ive been doing this test for 3 hours xD

Answer 77

oh I can't help with tests

Answer 78

that's something you need to do on your own

Answer 79

Its a pre-test, not the actual thang.

Answer 80

then getting it wrong doesn't hurt your grade as it helps the teacher see where you are in terms of the content

if you get it right, then the teacher doesn't need to go over it
if you get it wrong, then the teacher will know where to focus his/her energy

so either way, you'll be fine

Answer 81

Naw, this goes against my grade. Because i just learned it. so we have to take this, before we take our ACTUAL test. which really sucks. because im a very unfortunate when it comes to math, and if i dont get help, i fail.