Math Unit 6 Test

Question 1

Periodic Function:

Answer 1

• a consistent, repetitive pattern of y-values for incremental changes in x-values
• repeats at regular intervals

Question 2

Cycle:

Answer 2

ONE concrete pattern (the portion of the graph that repeats)

Question 3

Period:

Answer 3

the horizontal length of one cycle (p=360°/k for the Trig Graphs)

Question 4

Amplitude:

Answer 4

• the height going from “the middle horizontal line” (equation of the axis) to your maximum or minimum value
• A = (max value - min value) ÷ 2
• or A = max value - # equation of the axis

Question 5

Equation of the Axis:

Answer 5

• the horizontal line that divides the graph in half, notice it does not have to be symmetrical
• y = max value + min value/2

Question 6

Periodic:

Answer 6

• The shape of the graph repeats over some interval
• Repetitive y-values for consistent increases of x-values

Question 7

Non-periodic:

Answer 7

No repeated pattern on y-values

Question 8

y = sin x

Answer 8

middle, up, middle, down, middle

Question 9

Key Properties: f(x) = sin x

Answer 9

Amplitude: 1 - (1-(-1)/2)
y-intercept: (0,0)
Maximum: 1
Domain: {x ∈ R}
Equation of the axis: y = 0
Period: 360°
x-intercept: (0°,0), (180°,0), (360°,0)
Minimum: -1
Range: {y ∈ R | -1≤ y ≤ 1}

Question 10

f(x) = sin x, five key points:

Answer 10

(0°,0) (90°,1) (180°,0) (270°,-1) (360°,0)

Question 11

y = cos x

Answer 11

up, middle, down, middle, up

Question 12

Key Properties: f(x) = cos x

Answer 12

Amplitude: 1 (1-(-1)/2)
y-intercept: (0,1)
Maximum: 1
Domain: {x ∈ R}
Equation of the axis: y = 0
Period: 360°
x-intercept: (90°,0), (270°,0)
Minimum: -1
Range: {y ∈ R | -1≤ y ≤ 1}

Question 13

f(x) = cos x, five key points:

Answer 13

(0°,1) (90°,0) (180°,-1) (270°,0) (360°,1)

Question 14

How are these functions alike and different? (sin & cos)

Answer 14

Same curve pattern, same period, the same maximum and minimum value
y = cos x is a 90° shift to the left of the y = sin x

Question 15

Amplitude:
(lesson 3)

Answer 15

the height from the center line to the peak (or to the trough)
the height from highest to lowest points divided by 2

Question 16

Period:
(lesson 3)

Answer 16

goes from one peak to the next (or from any point to the next matching point)

Question 17

Summary - The graph y = a sin kx will have:

Answer 17

Amplitude: a
Period: 360°/k
Range: {yER| -a ≤ y ≤ a}

Question 18

will have… amplitude:

Answer 18

a

Question 19

will have… period:

Answer 19

360/k

Question 20

Range:

Answer 20

{yER| -a ≤ y ≤ a}

Question 21

Vertical Stretch and Compression will affect the ? and the ?

Answer 21

amplitude
range

Question 22

Horizontal Stretch and Compression will affect the ? (the x-values)

Answer 22

period

Question 23

Summary - The graph y = a cos kx will have:

Answer 23

Amplitude: a
Period: 360°/k
Range: {yER| -a ≤ y ≤ a}

Question 24

mapping notation

Answer 24

(1/kx + d, ay + c)

Question 25

formula

Answer 25

fx = asin(k(x-d)) + c
fx = acos(k(x-d)) + c

Question 26

factor out

Answer 26

k

Question 27

if (x-d) d is..
if (x+d) d is..

Answer 27

positive
negative

Question 28

When graphing determine the intervals of the key points using the PERIOD

Answer 28

Determine the PERIOD (360/k)
DIVIDE the PERIOD by 4 to determine the intervals along the x-axis
Use the ‘a’ value to determine the value on the y-axis

Question 29

The “a”

Answer 29

• Vertical stretch or compression
• If ‘a’ is negative, there is a reflection along the x-axis

Question 30

The “k”

Answer 30

• Horizontal stretch or compression
• If ‘k’ is negative, there is a reflection along the y-axis

Question 31

The “d’

Answer 31

• Horizontal translation (shift left or right) ** phase shift **

Question 32

The “c”

Answer 32

• Vertical translation (shift up or down)

Question 33

Which variable represents the amplitude?

Answer 33

a (always positive)

Question 34

Which variable represents the equation of the axis?

Answer 34

c

Question 35

Which variable affects the period?

Answer 35

k

Question 36

Which variable(s) affect the domain?

Answer 36

d and k

Question 37

Which variable(s) affect the range?

Answer 37

a and c

Question 38

Domain of one cycle

Answer 38

{xER|phaseshift ≤ x ≤ phaseshift + period}
(d) (d + p)

Question 39

Range:

Answer 39

{yER| c - amplitude ≤ y ≤ c + amplitude}

Question 40

y = -sinx

Answer 40

(Begins on the equation of the axis and goes DOWN)

Question 41

y = -cosx

Answer 41

(Begins on the MINIMUM point)

Question 42

Modelling Sinusoidal Functions
When given graph Steps:

Answer 42

Find the max
Find the min
Find the a (max-min/2)
Find the period
Find the k (360/p)
Find the eq/n of axis - middle point
D will depend on if its cos or sin

Question 43

Modelling Sinusoidal Functions
When given words steps:

Answer 43

Write down a
Find eq’n of the axis by doing (max - a)
Find k by doing (360/period)
D again depends

Question 44

Modelling Sinusoidal Functions
When given table steps:

Answer 44

Max
Min
A (max-min/2)
Period
K (360/p)
eq’n of the axis by doing (max - a)
D depends

Question 45

For Ferris wheel:

Answer 45

Max
Min
Period = how long it takes for one full rotation
Interval = divide period by 4
Use how many revolutions to see the ending x value and how many times the cycle should repeat
K - 360/period
Y = (max + min/2)

Question 46

period in ferris wheel

Answer 46

P = minutes x seconds

Question 47

k in ferris wheel

Answer 47

K = 360/p

Question 48

If k increases, horizontal ? for blank minutes
If k decreases, horizontal ?for blank minutes

Answer 48

from og equation
compression
stretch

Question 49

What does the amplitude represent in Ferris wheel?

Answer 49

The amplitude represents the RADIUS of the ferris wheel

Question 50

How fast is someone sitting on the Ferris Wheel moving in m/s? (d is distance around/circumference)

Answer 50

d = 2PiR
D = circumference

S = d/t
S = circumference/period

Question 51

To figure out the depth of the water sub in the

Answer 51

t value

Question 52

To find period when not mentioned do

Answer 52

2 x the bigger seconds - the smaller 2(bs - ss)