0 A Review Of Basic Algebra 1 Equations And Inequalities 2 Functions And Graphs 3 Functions 4 Polynomial And Rational Functions 5 Exponential And Logarithmic Functions 6 Linear Systems 7 Conic Sections And Quadratic Systems 8 Sequences, Series, And Probability Chapter3: Functions
3.1 Graphs Of Functions 3.2 Transformations Of The Graphs Of Functions 3.3 More On Functions; Piecewise-defined Functions 3.4 Operations On Functions 3.5 Inverse Functions 3.CR Chapter Review 3.CT Chapter Test 3.CM Cumulative Review Exercises Section3.3: More On Functions; Piecewise-defined Functions
Problem 1SC: Classify the function as being even, odd, or neither. Problem 2SC Problem 3SC Problem 4SC Problem 5SC Problem 6SC Problem 7SC Problem 8SC Problem 9SC Problem 10SC Problem 1E: Fill in the blanks. If the graph of a function is symmetric about the ___________, it is called an... Problem 2E Problem 3E Problem 4E Problem 5E: Fill in the blanks. If the values of fx get larger as x increases on an interval, we say that the... Problem 6E: Fill in the blanks. If the values of fx get smaller as x increases on an interval, we say that the... Problem 7E: Fill in the blanks. If the values of fx do not change as x increases on an interval, we say that the... Problem 8E Problem 9E: Fill in the blanks. A local ________ occurs where a function changes from decreasing to increasing. Problem 10E Problem 11E: Determine whether each function even, odd, or neither. Problem 12E Problem 13E: Determine whether each function even, odd, or neither. Problem 14E: Determine whether each function even, odd, or neither. Problem 15E: Determine whether each function even, odd, or neither. Problem 16E: Determine whether each function even, odd, or neither. Problem 17E: Determine algebraically whether each function is even, odd, or neither. fx=x4+x2 Problem 18E: Determine algebraically whether each function is even, odd, or neither. fx=x3-2x Problem 19E: Determine algebraically whether each function is even, odd, or neither. fx=x3+x2 Problem 20E: Determine algebraically whether each function is even, odd, or neither. fx=x6-x2 Problem 21E: Determine algebraically whether each function is even, odd, or neither. fx=x5+x3 Problem 22E: Determine algebraically whether each function is even, odd, or neither. fx=x3-x2 Problem 23E: Determine algebraically whether each function is even, odd, or neither. fx=2x3-3x Problem 24E: Determine algebraically whether each function is even, odd, or neither. fx=4x2-5 Problem 25E: Determine algebraically whether each function is even, odd, or neither. fx=xx2-1 Problem 26E: Determine algebraically whether each function is even, odd, or neither. fx=2xx2-9 Problem 27E: Determine algebraically whether each function is even, odd, or neither. fx=1x4 Problem 28E: Determine algebraically whether each function is even, odd, or neither. fx=-2x2 Problem 29E: Determine algebraically whether each function is even, odd, or neither. fx=x+1 Problem 30E: Determine algebraically whether each function is even, odd, or neither. fx=2x-5 Problem 31E: Determine algebraically whether each function is even, odd, or neither. fx=xx Problem 32E: Determine algebraically whether each function is even, odd, or neither. fx=2x-x Problem 33E: State the open intervals where each function is increasing, decreasing, or constant. Problem 34E: State the open intervals where each function is increasing, decreasing, or constant. Problem 35E: State the open intervals where each function is increasing, decreasing, or constant. Problem 36E: State the open intervals where each function is increasing, decreasing, or constant. Problem 37E: State the open intervals where each function is increasing, decreasing, or constant. Problem 38E: State the open intervals where each function is increasing, decreasing, or constant. Problem 39E: Use the graph to identify any local maxima and local minima. Problem 40E: Use the graph to identify any local maxima and local minima. Problem 41E: Use the graph to identify any local maxima and local minima. Problem 42E: Use the graph to identify any local maxima and local minima. Problem 43E: Use the graph to identify any local maxima and local minima. Problem 44E: Use the graph to identify any local maxima and local minima. Problem 45E: Use the graph to identify any local maxima and local minima. Problem 46E: Use the graph to identify any local maxima and local minima. Problem 47E: Use the graph to identify any local maxima and local minima. Problem 48E: Use the graph to identify any local maxima and local minima. Problem 49E: Evaluate each piecewise-defined function. fx=2x+2ifx03ifx0 a. f-2 b. f0 Problem 50E: Evaluate each piecewise-defined function. fx=x-2ifx1x2ifx1 a. f-1 b. f5 Problem 51E: Evaluate each piecewise-defined function. fx=2ifx02-xif0x2x+1ifx2 a. f-1 b. f1 c. f2 Problem 52E: Evaluate each piecewise-defined function. fx=2xifx03-xif0x2xifx2 a. f-0.5 b. f0 c. f2 Problem 53E: Graph each piecewise-defined function. fx=x+2ifx<02ifx0 Problem 54E: Graph each piecewise-defined function. fx=2xifx<0-2xifx0 Problem 55E: Graph each piecewise-defined function. fx=xifx02ifx0 Problem 56E: Graph each piecewise-defined function. fx=-xifx<012xifx>0 Problem 57E: Graph each piecewise-defined function. fx=-4-xifx13ifx1 Problem 58E: Graph each piecewise-defined function. fx=-5-xifx1-3ifx1 Problem 59E: Graph each piecewise-defined function. fx=-xifx<0x2ifx0 Problem 60E Problem 61E Problem 62E Problem 63E Problem 64E Problem 65E Problem 66E Problem 67E Problem 68E Problem 69E Problem 70E: Graph each function. y=x+2 Problem 71E Problem 72E Problem 73E Problem 74E: Riding in a taxi A taxicab company charges 3 for a trip upto 1 mile, and 2 for every extra mile or... Problem 75E Problem 76E: iPad repair There is a charge of 30, plus 40 per hour or fraction of an hour, to repair an iPad.... Problem 77E: Rounding numbers Measurements are rarely exact; they are often rounded to an appropriate precision.... Problem 78E Problem 79E Problem 80E Problem 81E Problem 82E Problem 83E Problem 84E Problem 85E: Describe what happens at the point where the graph of a function changes from increasing to... Problem 86E Problem 87E Problem 88E Problem 89E Problem 90E Problem 91E Problem 92E Problem 93E Problem 94E Problem 95E Problem 96E: Determine if the statement is true or false. If the statement is false, then correct it and make it... Problem 97E Problem 98E: Determine if the statemment is true or false. If the statement is false, then correct it and make it... Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it... Problem 100E: Determine if the statement is true or false. If the statement is false, then correct it and make it... Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Real analysis
Please prove with these steps.
Transcribed Image Text: Function contraction theorem
Let (X, d) be a complete metric space.
Suppose that f: XX satisfies
d(f(x), f(y)) ≤ 2-¹d(x, y) for all x, y E X.
Show that there exists a unique point x* EX such that f(x*) = x*.
Problem 5 Hint:
i=0
Step 1. Let xo E X. Define a sequence {x} by the recurrence relation
xi = f(xi-1) for i=1,2,....
Step 2. Show that {x}
Step 3. Show that x* is the point of interest.
converges to a point x* by showing that it is Cauchy.
Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.
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