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? \( f(x)=-10 \cos (3 x)+10 \) \( f(x)=10 \cos \left(\frac{2 \pi}{3} x\right)+10 \) \( f(x)=10 \cos (3 x)-10 \) \( f(x)=-10 \cos \left(\frac{2 \pi}{3} x\right)+10 \)
Solution
Step 1 ：\(f(x) = a \cos (bx) + c\)
Step 2 ：\(a=-10, b=\frac{2 \pi}{3}, c=10\)
Step 3 ：\(f(x)=-10 \cos \left(\frac{2 \pi}{3} x\right)+10\)
