The graphed cosine function is the second one:
y = 0.5*cos(4 (x + pi/2) ) - 2
Which is the graphed function?
If we look at the graph, we can notice that:
- The y-intercept is at y = -1.5, and it is a maximum.
- The midline is at y = -2
- The amplitude is 0.5
- Between -pi and pi there are 5 maximums.
Because of the midline restriction, we discard options 1 and 3.
Because between 0 and pi there are 5 maximums, we know that the factor that multiplies the variable inside the cosine is 4.
The second option can be rewriten as:
y = 0.5*cos(4*(x + pi/2)) - 2
0.5*cos(4*x + 2pi)) - 2
And the period of the cosine function is 2pi, so the phase 2pi does not affect, then:
0.5*cos(4*x + 2pi)) - 2 = 0.5*cos(4*x) - 2
So this is the correct option.
If you want to learn more about cosine functions:
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