Question

Throughout the day, the depth of water at the end of a dock varies with the tides. The function h(t)=5cos(0.5t-2)+7 represents the height, in feet, of the water t hours after midnight. Which graph shows the height of the water at the dock at any time after midnight?

Answer 1

Remember that for a graphic of a trigonometric functions of the form $f(x)=Acos(Bx+C)+D$
$A$ is the amplitude of the function 
$f(x)=D$ is the midline of the trigonometric function 

We know form our problem that $A=5$, so the amplitude of our function is 5. We also know that the $D=7$. So the midline of our function is the line $h(t)=7$. 

Using those two features we can conclude that the graph that shows the height of the water at the dock at any time after midnight is: