College Algebra 1st Edition
ISBN: 9781938168383
Author: Jay Abramson
Publisher: Jay Abramson
1 Prerequisites 2 Equations And Inequalities 3 Functions 4 Linear Functions 5 Polynomial And Rational Functions 6 Exponential And Logarithmic Functions 7 Systems Of Equations And Inequalities 8 Analytic Geometry 9 Sequences, Probability And Counting Theory Chapter6: Exponential And Logarithmic Functions
6.1 Exponential Functions 6.2 Graphs Of Exponential Functions 6.3 Logarithmic Functions 6.4 Graphs Of Logarithmic Functions 6.5 Logarithmic Properties 6.6 Exponential And Logarithmic Equations 6.7 Exponential And Logarithmic Models 6.8 Fitting Exponential Models To Data Chapter Questions Section6.2: Graphs Of Exponential Functions
Problem 1TI: Sketch the graph of f(x)=4x. State the domain, range, and asymptote. Problem 2TI: Try it # 2 Graph f(x)=2x1+3. State domain, range, and asymptote. Problem 3TI: Solve 4=7.85(1.15)x2.27 graphically. Round to the nearest thousandth. Problem 4TI: Sketch the graph of f(x)=12(4)x. State the domain, range, and asymptote. Problem 5TI: Find and graph the equation for a function, g(x) , that reflects f(x)=1.25x about the y-axis. State... Problem 6TI: Write the equation for function described below. Give the horizontal asymptote, the domain, andthe... Problem 1SE: What role does the horizontal asymptote of anexponential function play in telling us about the... Problem 2SE: What is the advantage of knowing how to recognizetransformations of the graph of a parent... Problem 3SE: The graph of f(x)=3x is reflected about the y-axisand stretched verticallyby a factor of 4. What... Problem 4SE: The graph of f(x)=(12)x is reflected about they-axis and compressed vertically by a factor of 15.... Problem 5SE: The graph of f(x)=10x is reflected about the x-axisand shifted upward 7 units. What is the equation... Problem 6SE: The graph of f(x)=(1.68)x is shifted right 3 units,stretched vertically by a factor of 2, reflected... Problem 7SE: The graph of f(x)=2(14)x20 is shifted downward 4 units, and then shifted left 2 units,stretched... Problem 8SE: For the following exercises, graph the function and its re?ection about the y -axis on the same... Problem 9SE: For the following exercises, graph the function and its re?ection about the y -axis on the same... Problem 10SE: For the following exercises, graph the function and its re?ection about the y -axis on the same... Problem 11SE: For the following exercises, graph each set of functions on the same axes. f(x)=3(14)x,g(x)=3(2)x,... Problem 12SE: For the following exercises, graph each set of functions on the same axes. f(x)=14(3)x,g(x)=2(3)x,... Problem 13SE: For the following exercises, match each function with one of the graphs in Figure 12. f(x)=2(0.69)x Problem 14SE: For the following exercises, match each function with one of the graphs in Figure 12. 14.... Problem 15SE: For the following exercises, match each function with one of the graphs in Figure 12. Problem 16SE: For the following exercises, match each function with one of the graphs in Figure 12. f(x)=4(1.28)x Problem 17SE: For the following exercises, match each function with one of the graphs in Figure 12. f(x)=2(1.59)x Problem 18SE: For the following exercises, match each function with one of the graphs in Figure 12. f(x)=4(0.69)x Problem 19SE: For the following exercises, use the graphs shown in Figure 13. All have the form f(x)=abx. Which... Problem 20SE: For the following exercises, use the graphs shown in Figure 13. All have the form f(x)=abx. Which... Problem 21SE: For the following exercises, use the graphs shown in Figure 13. All have the form f(x)=abx. Which... Problem 22SE: For the following exercises, use the graphs shown in Figure 13. All have the form f(x)=abx. Which... Problem 23SE: For the following exercises, graph the function and its re?ection about the x -axis on the same... Problem 24SE: For the following exercises, graph the function and its re?ection about the x -axis on the same... Problem 25SE: For the following exercises, graph the function and its reflection about the x-axis on the same... Problem 26SE: For the following exercises, graph the transformation of f(x)=2x. Give the horizontal asymptote, the... Problem 27SE: For the following exercises, graph the transformation of f(x)=2x. Give the horizontal asymptote, the... Problem 28SE: For the following exercises, graph the transformation of f(x)=2x. Give the horizontal asymptote, the... Problem 29SE: For the following exercises, describe the end behavior of the graphs of the functions. f(x)=5(4)x1 Problem 30SE: For the following exercises, describe the end behavior of the graphs of the functions. f(x)=3(12)x2 Problem 31SE: For the following exercises, describe the end behavior of the graphs of the functions. f(x)=3(4)x+2 Problem 32SE: For the following exercises, start with the graph of f(x)=4x. Then write a function that results... Problem 33SE: For the following exercises, start with the graph of f(x)=4x. Then write a function that results... Problem 34SE: For the following exercises, start with the graph of f(x)=4x. Then write a function that results... Problem 35SE: For the following exercises, start with the graph of f(x)=4x. Then write a function that results... Problem 36SE: For the following exercises, start with the graph of f(x)=4x. Then write a function that results... Problem 37SE: For the following exercises, start with the graph of f(x)=4x. Then write a function that results... Problem 38SE: For the following exercises, each graph is a transformation of y=2x. Write an equation describing... Problem 39SE: For the following exercises, each graph is a transformation of y=2x. Write an equation describing... Problem 40SE: For the following exercises, each graph is a transformation of y=2x. Write an equation describing... Problem 41SE: For the following exercises, find an exponential equation for the graph. Problem 42SE: For the following exercises, find an exponential equation for the graph. Problem 43SE: For the following exercises, evaluate the exponential functions for the indicated value of x .... Problem 44SE: For the following exercises, evaluate the exponential functions for the indicated value of x .... Problem 45SE: For the following exercises, evaluate the exponential functions for the indicated value of x .... Problem 46SE: For the following exercises, use a graphing calculator to approximate the solutions of the equation.... Problem 47SE: For the following exercises, use a graphing calculator to approximate the solutions of the equation.... Problem 48SE: For the following exercises, use a graphing calculator to approximate the solutions of the equation.... Problem 49SE: For the following exercises, use a graphing calculator to approximate the solutions of the equation.... Problem 50SE: For the following exercises, use a graphing calculator to approximate the solutions of the equation.... Problem 51SE: Explore and discuss the graphs of f(x)=(b)x and g(x)=(1b)x. Then make a conjecture about... Problem 52SE: Prove the conjecture made in the previous exercise. Problem 53SE: Explore and discuss the graphs of f(x)=4x,g(x)=4x2, and h(x)=(116)4x. Then make aconjecture about... Problem 54SE: Prove the conjecture made in the previous exercise. Problem 52SE: Prove the conjecture made in the previous exercise.
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Transcribed Image Text: Prove that 1² converges uniformly on R.
Σ
n=1 x4+n²
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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