which of the following functions illustrates ...

# Explanation: ## Step1: Recall amplitude - formula for trig functions For $y = A\sin(Bx - C)+D$ or $y = A\cos(Bx - C)+D$, the amplitude is $|A|$. For $y=\tan(Bx - C)+D$, it has no amplitude. ## Step2: Analyze option A For $y = 1+\sin x$, here $A = 1$, but this is just a vertical - shift (the $+ 1$), no change in amplitude from the basic $\sin x$ function which has amplitude $1$. ## Step3: Analyze option B For $y=-2\cos6x$, the coefficient of the cosine function is $A=-2$. The amplitude of the basic $\cos x$ function is $1$, and here the amplitude is $| - 2|=2$, which represents a change in amplitude. ## Step4: Analyze option C For $y=-2-\cos(x - \pi)$, the $-2$ is a vertical - shift and the $-\cos(x - \pi)$ is a reflection and a phase - shift, but no change in amplitude from the basic $\cos x$ function (amplitude $1$). ## Step5: Analyze option D The function $y = \tan2x$ is a tangent function. Tangent functions do not have an amplitude. # Answer: B. $y=-2\cos6x$