Question

3 fill in the blank 1 point the graph of the function ( f(x)=5 cos (2 x) ) is a reflection over the ( x )-axis of the graph of ( g(x)= ) type your answer... type your answer... type your answer... 4 fill in the blank 1 point high tides at a beach occur at intervals of 12 hours 25 minutes. yesterday, high tide was measured at 5 feet above sea level and low tide was measured at 1 foot above sea level. what is the amplitude of a cosine function modeling the depth of the water in feet as a function of time in hours? amplitude = type your answer... feet

Explanation:

Question 3

Step1: Reflection over x - axis rule

The rule for reflecting a function \(y = f(x)\) over the \(x\) - axis is \(y=-f(x)\). If \(f(x)=5\cos(2x)\) is a reflection over the \(x\) - axis of \(g(x)\), then \(f(x)=-g(x)\).

Step2: Solve for \(g(x)\)

If \(f(x) = 5\cos(2x)\) and \(f(x)=-g(x)\), then \(g(x)=- 5\cos(2x)\)

Step1: Amplitude formula for cosine function

The formula for the amplitude \(A\) of a cosine function \(y = A\cos(Bx - C)+D\) (modeling a periodic phenomenon like tides) when given the maximum value \(M\) and minimum value \(m\) is \(A=\frac{M - m}{2}\)

Step2: Identify \(M\) and \(m\)

The maximum value (high - tide) \(M = 5\) feet and the minimum value (low - tide) \(m = 1\) foot.

Step3: Calculate the amplitude

Substitute \(M = 5\) and \(m = 1\) into the formula \(A=\frac{M - m}{2}=\frac{5 - 1}{2}\)

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Answer:

\(-5\cos(2x)\)

Question 4