+0  
 
0
363
5
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What are the phase shift and the vertical shift for the function f(x) = cos 4(x+5) + 3?

Guest Oct 2, 2014

Best Answer 

 #5
avatar+87293 
+5

Here's my take on this one :

Melody is correct

The amplitude is 1

The vertical shift is "up' 3 units

The horizontal shift is to the left by 5 rads

Note that the "4" tells us how many periods there are in 2pi...thus, the normal cosine graph is 'compressed" by a factor of 4 !!!

Here are the normal cosine graph and our function plotted on the same graph for comparison......https://www.desmos.com/calculator/5z1bg10apu

 

 

 

CPhill  Oct 3, 2014
 #1
avatar+17744 
+5

The 4 represents amplitude.

The +5 represents a horizontal shift.     ***

The +3 represents a vertical shift.        ***

A change in period  would be represented by a multiplier of the x term, as in:  y  =  sin(3x), which Since this problem as simply x, or 1x, there is no increase or decrease in the period.

geno3141  Oct 2, 2014
 #2
avatar
0

Which direction are they going? 

Guest Oct 2, 2014
 #3
avatar+92751 
0

+ means in the positive direction, up and right.

Melody  Oct 3, 2014
 #4
avatar+92751 
+5

 Gino, my answers are a bit  different from yours - would you like to check?

 

f(x) = cos 4(x+5) + 3?

 

Amplitude is 1

vertical shift is 3 units up   +3

wavelength = 2pi/4 = pi/2

Phase shift is 5 to the left    (-5)   

To find the shift I say x+5=0   so x=-5

 

 

The green line is meant to be a arrow going left.

Melody  Oct 3, 2014
 #5
avatar+87293 
+5
Best Answer

Here's my take on this one :

Melody is correct

The amplitude is 1

The vertical shift is "up' 3 units

The horizontal shift is to the left by 5 rads

Note that the "4" tells us how many periods there are in 2pi...thus, the normal cosine graph is 'compressed" by a factor of 4 !!!

Here are the normal cosine graph and our function plotted on the same graph for comparison......https://www.desmos.com/calculator/5z1bg10apu

 

 

 

CPhill  Oct 3, 2014

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