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

Guest Oct 2, 2014

#5**+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**+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

#4**+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**+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