Exam Questions: Mathematics and Calculus, Exams of Mathematics

Download Exam Questions: Mathematics and Calculus and more Exams Mathematics in PDF only on Docsity! MA113:004{006 Russell Brown Exam 1 22 September 1998 Answer all of the following questions. Use the backs of the question papers for scratch paper. Additional sheets are available if necessary. No books or notes may be used. When answering these questions, please be sure to 1) check answers when possible, 2) clearly indicate your answer and the reasoning used to arrive at that answer (unsupported answers may receive NO credit). If you use your calculator to solve an equation or produce a graph, please indicate this on your test paper. Otherwise the answer may receive no credit. Name Section Question Score Total 1 5 2 5 3 5 4 5 5 15 6 15 7 20 8 15 9 15 Total 100 1. If f(x) = x+ 1 and g(x) = p x, nd a formula for g  f . Give the domain of g  f . 2. Solve the equation 2x 2+1 = 8: 6. A population of critters doubles every 4 hours. At t = 0, there are 200 critters. (a) How many critters are there after 12 hours? (b) Write a function N(t) which gives the population after t hours. (c) What is the population after 13 hours? (d) When does the population contain 500 critters? You must explain how to answer this question algebraically. Do not use the Solve feature on your calculator. 7. Below is the graph of a function f(x). Use the graph to answer the following questions. (a) What is f(0)? What is the domain of f? (b) On the same axes, sketch the graph of f(x+ 2). Label the coordinates of the corner on the graph of f(x+ 2). (c) On the same axes, sketch the graph of f(2x + 2). Label the coordinates of the corner on the graph of f(2x + 2). (d) On the second set of axes, sketch the graph of f1(x). 8. Let f(x) = 2 + 1 x : (a) Find a formula for f1. (b) What is the domain of f and what is the domain of f1?