MTH 261 Test 1 Fall 2022.docx

MTH 261 Test 1 Name: ______________________________________ Date: _______________________ Directions: Complete the following questions below without using your book, notes, or any help. Do all problems that you know first. You may use your scientific calculator. You may write on this test page. Ple...

MTH 261 Test 1 Name: ______________________________________ Date: _______________________ Directions: Complete the following questions below without using your book, notes, or any help. Do all problems that you know first. You may use your scientific calculator. You may write on this test page. Please show ALL of your work. If little to no work is shown, you will receive a zero on that question. If only the answer is present, you will receive a zero on that question. Once you are done, please fold this paper in half vertically, and write your name and MTH 261 Campbell on the back. Please bring it up to Mrs. Coco and you may leave for the day. There are two sides to this test. Find the domain of the function $\frac{1}{3x^{2} - 27}$ If f(x) = 3x3 − 5x find the difference quotient using $\frac{f\left( x + h \right) - f(x)}{h}$ If f(x)= 4x3 and g(x) = 2x − 5 find C(x) = g(f(x)). Suppose that the graph of f(x) is given. In words, describe how the graph of the following function can be obtained from the graph of f(x) if the following transformations were applied: $$\frac{\mathbf{1}}{\mathbf{5}}\mathbf{f}\left( \mathbf{x -}\mathbf{5} \right)\mathbf{-}\mathbf{2}$$ Use the following transformations to sketch the graph of the function give below. Please graph your function on the x-y plane given below. Be sure to label all the important points that you used. f(x) = -4(x + 3)­­­­2 + 2 Suppose a ball is dropped from the upper observation deck of the CN Tower in Toronto, 450m above the ground. Estimate the speed of the ball after 5 seconds using Galileo’s law expressed by f(t) = 4.9t2 where t is the elapsed in seconds, and f(x) is measured in meters. Fill out the table below to find the average rate of speed of the ball on the below for the following intervals. Do not forget to label your columns: [5, 5.1], [5, 5.01], and [5.001]. Examine the time intervals given. What are we doing to the intervals to find the average rate of speed? What does the average rate of speed of the ball seem to be approaching as it t =5 seconds?