1. In a tiny country, the current population is 200,000 and is increasing at 2.5% per year. a. Is this situation describing a linear or exponential increase? Write several sentences to convince me of your answer. b. Write a function describing this situation, and sketch its graph. (Hint: It might help to start by making a table) c. The country can produce enough rice for 300,000 people. Assuming they continue to produce the same amount of rice each year, how long will it be before there are shortages in rice and they have to start importing it? 2. Let f(x) = sin(x) and g(x) = x -=. a. Find and graph f . g(x). Explain how this graph differs from the graph of sin(x). b. Find and graph g . f (x). Explain how this graph differs from the graph of sin(x). 3. Consider the equation g(x) = 3(x -2)2 - 4 and sketch its graph. a. Describe how this graph differs from that of y = x2. b. Determine the equation of the inverse of this equation and sketch its graph. Please show all work. 4. Let h(x) = -+3 x+9 a. What are the domain and range of h? b. Use sentences to describe the end behavior of h. C. Explain your reasoning for both. 5. Giveny = -3sin (x + 7) -4 a. Sketch the graph. b. Describe the domain and range. c. Write an equation for a graph that is a sine or cosine function shifted 3 units downward, having amplitude .65 and shifted - units to the left. i. Label your axes.6. Evaluate the following: a. 5in (E) b. cos() it. cost?) d. Sin() T. Let H E [D,2:r]. Find all the 1llalues B in radians AND degrees that satisfy the equations below. a. lo-SIZE}: - h. sinb'}: i 2 o. 1121:1113] = 1 3. Given the function x) = x2 13 a. State the domain and range of f'1(x) h. Sketch a graph of x} and f'x]