Question 1

Create your own function. Create the graph for a rational function so that it has a vertical asymptote, a horizontal asymptote, a hole, and a combination of x and/or y-intercepts. Show all work for your function and sketch the graph. You may create your own coordinate plane to adjust the scale. You must include the factored form and the standard form of your function (numerator and denominator each in standard form).

Question 2

The water level relative to the top of a boat dock varies with the tides. One particular day, low tide occurs at midnight and the water level is 7 ft below the dock. The first high tide of the day occurs at approximately 6:00 a.m. and the water level is 3 ft below the dock. The next low tide occurs at noon and the water leve is again 7 ft below the dock. Assume this pattern continues...

A) Complete the table of values for the water level from midnight to noon

B) Sketch a graph for the water level from midnight to noon

C) Write a function of the form w(t) = A cos (Bt-C) + D, where w(t) is the water level (in ft) relative to the top of the dock, t hours after midnight.