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)=

jjennylove Jan 18, 2019

#1**+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

CPhill Jan 18, 2019

#2**+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

CPhill Jan 18, 2019

#3**+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

CPhill Jan 18, 2019

#7**+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**+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 !!!!

CPhill
Jan 18, 2019

#9**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**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...

CPhill
Jan 18, 2019

#4**+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

CPhill Jan 18, 2019

#5**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.

jjennylove
Jan 18, 2019

#6**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