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Question: iii function review 1 what requirement must be met for...

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III. Function Review 1. What requirement must be met for a mathematical relation to be a function? 2. Given the function f(x) -x2 - 5x +3, find and simplify the following: a. f(2) b. f(-6) c. f(h) d. fx +h) f(x+h)-f(x) e.

Math 1210 Prerequisite Review, Part i2 Name: Please use additional sheets of paper for this assignment. For full credit, the work must be legible and easy to follow I. The Basic Trigonometric Functions For each of the following functions: a. State the domain and range b. On the interval [-2T, 2T, state any intercepts as (x, y) ordered pairs c. Graph the function on the interval [-2T, 2 . Be sure to indicate amplitude where appropriate and show any intercepts and asymptotes. DO NOT use graphing technology! 2. У-cos x 3. y-tan x 6. y-cot x II. Solving Equations Solve each equation below, showing all steps in a clear and logical order. Answers must be exact (not approximations). Answers for trigonometric equations must be given in radians. 1. 5x2-2x 10 3. In(3x 1)-4 5. arcsin-=x

Some of the most important algebraic simplifications will answer questions like what is ? What happens when you divide very large numbers? Or what happens when you subtract very large numbers? -x-6 I. Consider . a. What happens whenx-3? x-2.999? x-3.001? Now, factor and reduce this fraction. b. Now what happens to the reduced fraction when x-3? 2x6 Will look like at x 3? c. What do you think the graph of f(x) - 5 2. Consider3x2 a. What happens when x--1? x=-0.999? x=-1.001? Now find a common denominator and subtract b. Now what happens whenx1? 5 What do you think the graph of f(x) will look lik c. e x2-3x+2 x2-1 near x =-1 ? x-16 2. Consider K-4 a. What happens when x=4? x=3.999? x-4.001? Now, rationalize the denominator and simplify the fraction. b. Now what happens when x-4 x2-16 c. What do you think the graph of f(x) will look like near x-4?

Name Activity - The Notion of a Limit On a separate sheet of paper, label by part and letter and answer the following questions and then attach to this assignment. Part 1. Suppose that g is the function given by the graph below. Use the graph to answe r each of the following questions. (a) Determine the values g(-2), g(-1), g(0), g(1), and g(2), if defined. If the function value is not defined, explain what feature of the graph tells you this. (b) For each of the values a =-1, a = 0, and a-2, complete the following sentence: As x gets closer and closer (but not equal) to a, g(x) gets as close as we want to (c) What happens as x gets closer and closer (but not equal) to a = 1? Does the function g(x) get as close as we would like to a single value? Figure: Graph of y - g(x) Part 2. Sketch each graph on the provided axes of a function that has all of the stated properties y -f(r) such that ·f(-2) = 2 and lim,f(x)-1 .f(-1) 3 and lim f(x)-3 14-2 f(1) is not defined and lim f(x) = 0 .f(2) 1 and lim f(x) does not exist.

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