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