+50 Can someone please walk me through step by step on how to graph y= -3 cos (2(x - pi/4))-1
+23251 The standard graph is y = cos(x)
In the equation y = -3(cos(2(x - pi/4) - 1:
The negative sign flips the graph vertically.
The 3 changes the amplitude, stretching it vertically by a factor of 3.
The 2 changes the period. The original period is 2pi, now it is 2pi/2 = pi.
So the new function has one-half the period of the old function.
The pi/4 translates the graph horizontally by the amount after the negative sign. Since the 'x' has been changed to 'x - pi/4', the graph has been moved to the right by pi/4.
If the change had been from 'x' to 'x + pi/3', the graph would be moved to the left by pi/3.
The -1 translates the graph vertically, moving the graph down 1.
The graph y = cos(x) has a max at (0,1), a min at (pi,-1) and a max at (2pi,1).
It has a period of 2pi and an amplitude of 1.
The graph y = -cos(x) flips the graph vertically; therefore it has a min at (0,-1), a max at (pi,1) and a min at (2pi,-1).
In comparison to the previous graph, its period and amplitude has not changed.
The graph y = -3cos(x) increases the amplitude by 3. It has a min at (0,-3), a max at (pi,3), and a min at (2pi,-3).
In comparison to the previous graph, its period is not changed.
The graph y = -3cos(x) -1 translates the graph down one. It has a min at (0,-4), a max at (pi,2), and a min at (2p,-2).
In comparison to the previous graph, its period and amplitude is not changed.
The graph y = -3cos(x - pi/4) - 1 translates the graph to the right by pi/4. It has a max at (pi/4,-4), etc.
In comparison to the previous graph, its period and amplitude is not changed.
The graph y = -3co(2(x - pi/4)) - 1 changes the period; the period is now only pi (found by taking the original period of 2pi and dividing that by 2, giving a period of 2pi/2 = pi.)
In comparison to the previous graph, its period has changed, but not the amplitude.
