Problem

A cosine function has a period of 3 , a maximum value of 20 , and a minimum value of 0 . The function is a reflection of its parent function over the \( x \)-axis.
Which function could be the function described?
\( f(x)=-10 \cos (3 x)+10 \)
\( f(x)=10 \cos \left(\frac{2 \pi}{3} x\right)+10 \)
\( f(x)=10 \cos (3 x)-10 \)
\( f(x)=-10 \cos \left(\frac{2 \pi}{3} x\right)+10 \)

Answer

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Answer

\(f(x)=-10 \cos \left(\frac{2 \pi}{3} x\right)+10\)

Steps

Step 1 ：\(f(x) = a \cos (bx) + c\)

Step 2 ：\(a=-10, b=\frac{2 \pi}{3}, c=10\)

Step 3 ：\(f(x)=-10 \cos \left(\frac{2 \pi}{3} x\right)+10\)

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