Answer:
y - intercept is 3 is true.
Step-by-step explanation:
At y - intercept, x = 0, therefore,
y = 3cos2(0)
y = 3cos 0
y = 3.
Therefore, y - intercept is 3 is true.
The amplitude ( maximum vertical displacement of the graph) is 3 not - 3.
The range of the function y = 3cos(2x) is [-3,3] but not [0,3].
Period is the time taken for a complete oscillation and it is measured in seconds, since we were given that the period is 2π then it is false because it is not measured in seconds. Therefore, the wavelength (one complete oscillation) is π.
Answer:
A) The y-intercept is 3.
Step-by-step explanation:
The general form of the cosine function is:
[tex]y=A\cos (B(x+C))+D[/tex]
where:
In the case of y = 3 cos (2x):
Therefore, the amplitude is 3 and the midline is y = 0.
The maximum value of the function is the midline plus the amplitude (0 + 3 = 3), while the minimum value of the function is the midline minus the amplitude (0 - 3 = -3). Therefore, the range of the function is [-3, 3].
To calculate the period, substitute B = 2 into the period formula:
[tex]\textsf{Period}=\dfrac{2\pi}{B}=\dfrac{2\pi}{2}=\pi[/tex]
Therefore, the period is π.
The y-intercept is the point at which the curve intersects the y-axis, so when x = 0. A peak of the parent cosine function y = cos(x) occurs at x = 0. Since the given function has no phase shift, its peak will also occur at x = 0. As the maximum value of the function is y = 3, the y-intercept is 3.
The y-intercept is the point where the curve intersects the y-axis, which occurs when x = 0. A peak of the parent cosine function y = cos(x) occurs at x = 0. Since the given function has no phase shift, its peak will also occur at x = 0. As the maximum value of the function is y = 3, the y-intercept is 3.
In summary, the true statement about the graph of y = 3 cos (2x) is:
[tex]\Large\boxed{\textsf{The $y$-intercept is 3.}}[/tex]
