+0  
 
0
164
10
avatar+600 

If any is willing to help me with these ,I need the help.

 

1) What is the equation of the midline for the function f(x) ?

 

f(x)= 1/ 2 cos (x) + 5

 

 

2)

What is the frequency of the function f(x)?

 

f(x)=1/4 cos(2x)+5

 

Express the answer in fraction form.

 

 

3)

The functionf(x) is multiplied by a factor of 2 and then 3 is added to the function. 

 

f(x)=sin(x)

What effect does this have on the graph of the function?

 

A) The graph is vertically stretched by a factor of 2 and shifted up 3 units.

B)The graph is vertically stretched by a factor of 3 and shifted up 2 units.

C)The graph is vertically compressed by a factor of 3 and shifted up 2 units.

D) The graph is vertically compressed by a factor of 2 and shifted up 3 units.

 

4)

The graph of  f(x)=sin(x)  is transformed to a new function, g(x) , by stretching it vertically by a factor of 2 and shifting it 3 units up.

What is the equation of the new function  g(x) ?

 

Enter your answer

g(x)=

 Jan 18, 2019
edited by jjennylove  Jan 18, 2019
edited by jjennylove  Jan 18, 2019
edited by jjennylove  Jan 18, 2019
 #1
avatar+96208 
+2

1) What is the equation of the midline for the function f(x) ?

 

f(x)= 1/ 2 cos (x) + 5

 

Notice that   the min for the cos  = -1

So....the lowest point on the graph  is (1/2)(-1) + 5  = -1/2 + 5 =  4.5

 

The max for the cos  = 1

So...the highest point on the graph  = (1/2)(1) + 5 = 5.5

 

Midline    ( Highest point + Lowest point) / 2   =    (5.5 + 4.5) / 2  =  10 / 2  =  5

So....the equation for the midline is  y = 5

 

cool cool cool

 Jan 18, 2019
 #2
avatar+96208 
+2

2)

What is the frequency of the function f(x)?

f(x)=1/4 cos(2x)+5

Express the answer in fraction form.

 

In the form

 

A * trig function ( Bx + C) + D

 

Only  "B" affects the period

 

Here...B  = 2      [ and  C = 0 ]

 

This means that there are 2 periods in 2pi

 

So....to find the period  take    2pi / 2    =   pi = the period

 

And the frequency  =  1 / period  =   1 /pi

 

 

cool cool cool

 Jan 18, 2019
 #3
avatar+96208 
+2

3)

The functionf(x) is multiplied by a factor of 2 and then 3 is added to the function. 

 

f(x)=sin(x)

What effect does this have on the graph of the function?

 

The "2"  vertically stretches the parent function by a factor of 2

The "3"  shifts the function up 3 units

 

So.... "A" is correct

 

 

cool cool cool

 Jan 18, 2019
 #7
avatar+600 
+1

So you know it is vertically stretched when there is on an (x) and the "B" (period) is not included and it is compressed when there is a value for B ? such as "4x" ?

jjennylove  Jan 18, 2019
 #8
avatar+96208 
+1

In the form

 

y = A * trig function (Bx  + C ) + D

 

The number on "B"  only affects the horizontal compression or horizontal expansion .....

 

If this  number  is between 0 and 1, we have a horizontal " stretch"

 

If this number is > 1, then we have a horizontal "compression"

 

It is "A"  that affects the vertcal stretching or vertical compression

 

If   absolute value of A  is  > 0  but < 1,  we have a vertical  compression

If absolute value of A > 1, we have a vertical stretch

 

"D"  affects the shift of the graph upward   (if D is positive)  or downward ( if D is negative)

 

Hope that helps, Jenny   !!!!

 

 

 

cool cool cool

CPhill  Jan 18, 2019
 #9
avatar+600 
0

ohhh that all makes sense now. However such as the problem I had , how did you know "x" was a vertical stretch since x does not have a value ?

jjennylove  Jan 18, 2019
 #10
avatar+96208 
0

Remember that we have

 

y =  2sin (x)  + 3

 

We can write this as

 

y = 2 sin (1x) + 3

 

So "B"  = 1.....this means that there is no horizontal stretch or compression

 

It is  "A"  [ the number in front of sin (x) ] that affects the vertical stretching or compression

Since the abs value of this  = 2...and this is > 1.......we have a "stretch"

If the abs value of "A"  is between 0 and 1, we would have a vertical compression...

 

 

cool cool cool

CPhill  Jan 18, 2019
 #4
avatar+96208 
+2

4)

The graph of  f(x)=sin(x)  is transformed to a new function, g(x) , by stretching it vertically by a factor of 2 and shifting it 3 units up.

What is the equation of the new function  g(x) ?

 

This is just the counterpart of the last question

 

g(x)  =   2sin (x) + 3

 

 

cool cool cool

 Jan 18, 2019
 #5
avatar+600 
0

I want to say thank you. These are great explantaions and it has helped me a lot. I am very thankful that you helped with each one. They were more easy then it looked. smiley

jjennylove  Jan 18, 2019
 #6
avatar+600 
0

Looking at the question I didnt realize it was simialr to the last question but now I do it was just the oppostite .

jjennylove  Jan 18, 2019

35 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.