How do you graph # y=4cos(2x-1)+3#?

1 Answer
Apr 1, 2018

Answer:

So features of graph

Amp:4
Period: #pi#
Max:7
Min:-1

graph{4cos(2x-1)+3 [-10, 10, -5, 5]}

Explanation:

Translation form of sine is

#Asin[B(x-C)]+D#

A~ Vertical stretch/Amp, y values get stretched by A
B~ Horizontal strech/Period, x values get stretched by #1/B#
C~ Horizontal translation/Phase shift, x values move over by C
D~ Vertical translation, y values up by D

So we know that if we put it in translation form it looks like

#4cos[2(x-1/2)]+3#

So we know that the original #sin(x)# has these features

Amp:1
Period:#2pi#
Max: 1
Min: -1

graph{sin(x) [-8.89, 8.886, -4.446, 4.446]}

So #4cos(x)# means the Amplitude becomes 4 meaning the max is 4 and min -4

So #4cos(2x)# means the period halves becoming #pi#

So #4cos[2(x-1/2)]# means the origin moves over by #1/2#

#4cos[2(x-1/2)]+3# means all the y values move up by 3 meaning the max is 7 and the min -1

So features of graph

Amp:4
Period: #pi#
Max:7
Min:-1

graph{4cos(2x-1)+3 [-10, 10, -5, 5]}