Question

Find the domain, period, range, and amplitude of the cosine function.

y = -6cos4x

Answer 1

This cart may help if you write the cosine function in the form shown.

Answer 2

A. domain = \[-\frac{ 1 }{ 2 } \le x \le \frac{ 1 }{ 2 } ; period = 6; range = -6 \le y \le 6 ; amplitude = \frac{ 1 }{ 2 }\]
B. \[domain = all real numbers ; period = \frac{ 1 }{ 2 } ; raange = -6 \le y \le 6; amplitude = 6\]
C. \[domain = all real numbers; period = \frac{ 1 }{ 2 } ; range = -6 \le y \le 6 ; amplitude = -6\]
D. \[domain = - \frac{ 1 }{ 2 } \le x \le \frac{ 1 }{ 2 } ; period = 6 ; range = -6 \le y \le 6 ; amplitude = \frac{ 1 }{ 2 }\]

Answer 3

that doesnt help i need someone to show me how to work it out.

Answer 4

I did not intend the chart as an answer. It is one way to think about the problem.

Answer 5

i dont get it though..

Answer 6

So the standard form of the cos function would be as follows \[y=Acos[\omega(x-d)]+q\] where A is your amplitude, ie the max distance of the wave from the axis, like the turning point, and its positive, because its a distance. so Amplitude = 6. (x-d) would mean a shift left or right, but not in your function. Range is the interval of y values that the function takes on. so in this case, it ranges from -6 to +6. just note that q in the equation shifts the graph up/or down, but there is no q in your case so the range is unchanged, [-6,6]. \[\omega = 2\pi/p\] where w is the frequency of the wave and p is the distance it takes for a complete cycle of the cos graph. in your case w =4 therefore\[4=2\pi/p \] so solving for period (p), we get: \[p=2\pi/\omega \] therefore: \[p=2\pi/4 \] therefore period =\[\pi/2\]
Hope that helps :)

Answer 7

thank you makes sense!!!