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 Chapter3: Functions
3.1 Functions And Function Notation 3.2 Domain And Range 3.3 Rates Of Change And Behavior Of Graphs 3.4 Composition Of Functions 3.5 Transformation Of Functions 3.6 Absolute Value Functions 3.7 Inverse Functions Chapter Questions Section: Chapter Questions
Problem 1RE: For the following exercises, determine whether the relation is a function. {(a,b),(c,d),(e,d)} Problem 2RE: For the following exercises, determine whether the relation is a function. 2.... Problem 3RE: For the following exercises, determine whether the relation is a function. y2+4=x , for x the... Problem 4RE: For the following exercises, determine whether the relation is a function. 4. Is the graph in Figure... Problem 5RE: For the following exercises, evaluate the function at the indicated values... Problem 6RE: For the following exercises, evaluate the function at the indicated values... Problem 7RE: For the following exercises, determine whether each functionsare one-to-one. 7. f(x)=3x+5 Problem 8RE: For the following exercises, determine whether each functions are one-to-one. f(x)=x3 Problem 9RE: For the following exercises, use the vertical line test to determine if the relation whose graph is... Problem 10RE: For the following exercises, use the vertical line test to determine if the relation whose graph is... Problem 11RE: For the following exercises, use the vertical line test to determine if the relation whose graph is... Problem 12RE: For the following exercises, graph the functions. 12. f(x)=|x+1| Problem 13RE: For the following exercises, graph the functions. f(x)=x22 Problem 14RE: For the following exercises, use Figure 2 to approximate the values. 14. f(2) Problem 15RE: For the following exercises, use Figure 2 to approximate the values. 15. f(2) Problem 16RE: For the following exercises, use Figure 2 to approximate the values 16. If f(x)=2 , then solve for... Problem 17RE: For the following exercises, use Figure 2 to approximate the values. 17. If f(x)=1 , then solve for... Problem 18RE: For the following exercises, use the function h(t)=16t2+80t to find the values. 18. h(2)h(1)21 Problem 19RE: For the following exercises, use the function h(t)=16t2+80t to find the values. 19. h(a)h(1)a1 Problem 20RE: For the following exercises, find the domain of each function, expressing answers using interval... Problem 21RE: For the following exercises, find the domain of each function, expressing answers using interval... Problem 22RE: For the following exercises, find the domain of each function, expressing answers using interval... Problem 23RE: For the following exercises, find the domain of each function, expressing answers using interval... Problem 24RE: For the following exercises, find the average rate of change of the functions from x=1tox=2 . 24.... Problem 25RE: For the following exercises, find the average rate of change of the functions from x=1tox=2 . 25.... Problem 26RE: For the following exercises, find the average rate of change of the functions from x=1tox=2 . 26.... Problem 27RE: For the following exercises, use the graphs to determine the intervals on which the functions are... Problem 28RE: For the following exercises, use the graphs to determine the intervals on which the functions are... Problem 29RE: For the following exercises, use the graphs to determine the intervals on which the functions are... Problem 30RE: For the following exercises, use the graphs to determine the intervals on which the functions are... Problem 31RE: For the following exercises, use the graphs to determine the intervals on which the functions are... Problem 32RE: For the graph in Figure 3, the domain of the function is [3,3] . The range is [10,10] . Find the... Problem 33RE: Find the absolute maximum of the function graphed in Figure 3. Problem 34RE: For the following exercises, find (fg)(x) and (gf)(x) for each pair of functions. 34.... Problem 35RE: For the following exercises, find (fg)(x) and (gf)(x) for each pair of functions. 35.... Problem 36RE: For the following exercises, find (fg)(x) and (gf)(x) for each pair of functions. 36.... Problem 37RE: For the following exercises, find (fg)(x) and (gf)(x) for each pair of functions. 37.... Problem 38RE: For the following exercises, find (fg)(x) and (gf)(x) for each pair of functions. 38.... Problem 39RE: For the following exercises, find (fg) and the domain for (fg)(x) for each pair of functions. 39.... Problem 40RE: For the following exercises, find (fg) and the domain for (fg)(x) for each pair of functions. 40.... Problem 41RE: For the following exercises, find (fg) and the domain for (fg)(x) for each pair of functions. 41.... Problem 42RE: For the following exercises, find (fg) and the domain for (fg)(x) for each pair of functions. 42.... Problem 43RE: For the following exercises, express each function H as a composition of two functions f and gwhere... Problem 44RE: For the following exercises, express each function H as a composition of two functions f and gwhere... Problem 45RE: For the following exercises, sketch a graph of the given function. 45. f(x)=(x3)2 Problem 46RE: For the following exercises, sketch a graph of the given function. 46. f(x)=(x+4)3 Problem 47RE: For the following exercises, sketch a graph of the given function. 47. f(x)=x+5 Problem 48RE: For the following exercises, sketch a graph of the given function. 48. f(x)=x3 Problem 49RE: For the following exercises, sketch a graph of the given function. 49. f(x)=x3 Problem 50RE: For the following exercises, sketch a graph of the given function. 50. f(x)=5x4 Problem 51RE: For the following exercises, sketch a graph of the given function. 51. f(x)=4[x26] Problem 52RE: For the following exercises, sketch a graph of the given function. 52. f(x)=(x+2)21 Problem 53RE: For the following exercises, sketch the graph of the function g if the graph of the functionfis... Problem 54RE: For the following exercises, sketch the graph of the function g if the graph of the functionfis... Problem 55RE: For the following exercises, write the equation for the standard function represented by each of the... Problem 56RE: For the following exercises, write the equation for the standard function represented by each of the... Problem 57RE: For the following exercises, determine whether each function below is even, odd, or neither. Problem 58RE: For the following exercises, determine whether each function below is even, odd, or neither. Problem 59RE: For the following exercises, determine whether each function below is even, odd, or neither. Problem 60RE: For the following exercises, analyze the graph and determine whether the graphed function is even,... Problem 61RE: For the following exercises, analyze the graph and determine whether the graphed function is even,... Problem 62RE: For the following exercises, analyze the graph and determine whether the graphed function is even,... Problem 63RE: For the following exercises, write ail equation tor the transformation of f(x)=|x| . Problem 64RE: For the following exercises, write ail equation tor the transformation of f(x)=|x| . Problem 65RE: For the following exercises, write ail equation tor the transformation of f(x)=|x| . Problem 66RE: For the following exercises, graph the absolute value function. Problem 67RE: For the following exercises, graph the absolute value function. Problem 68RE: For the following exercises, graph the absolute value function. Problem 69RE: For the following exercises, find f1(x) for each function. 69. f(x)=9+10x Problem 70RE: For the following exercises, find f1(x) for each function. 70. f(x)=xx+2 Problem 71RE: For the following exercise, find a domain on which the function f is one-to-one and non-decreasing.... Problem 72RE: For the following exercise, find a domain on which the function f is one-to-one and non-decreasing.... Problem 73RE: For the following exercises, use a graphing utility to determine whether each function is... Problem 74RE: For the following exercises, use a graphing utility to determine whether each function is... Problem 75RE: For the following exercises, use a graphing utility to determine whether each function is... Problem 76RE: For the following exercises, use a graphing utility to determine whether each function is... Problem 1PT: For the following exercises, determine whether each of the following relation is a function. y=2x+8 Problem 2PT: For the following exercises, determine whether each of the following relation is a function. 2.... Problem 3PT: For the following exercises, evaluate the function f(x)=3x2+2x at the given input. 3. f(2) Problem 4PT: For the following exercises, evaluate the function f(x)=3x2+2x at the given input. 4. f(a) Problem 5PT: For the following exercises, evaluate the function f(x)=3x2+2x at the given input. 5. Show that the... Problem 6PT: For the following exercises, evaluate the function f(x)=3x2+2x at the given input. Write the domain... Problem 7PT: For the following exercises, evaluate the function f(x)=3x2+2x at the given input. 7. Given... Problem 8PT: For the following exercises, evaluate the function f(x)=3x2+2x at the given input. 8. Graph the... Problem 9PT: For the following exercises, evaluate the function f(x)=3x2+2x at the given input. 9. Find the... Problem 10PT: For the following exercises, use the function f(x)=32x2+x and g(x)=x to find the composite... Problem 11PT: For the following exercises, use the function and to find the composite functions. 11. m:math... Problem 12PT: For the following exercises, use the function f(x)=32x2+x and g(x)=x to find the composite... Problem 13PT: For the following exercises, graph the functions by translating, stretching, and/or compressing a... Problem 14PT: For the following exercises, graph the functions by translating, stretching, and/or compressing a... Problem 15PT: For the following exercises, determine whether the functions are even, odd, or neither. 15.... Problem 16PT: For the following exercises, determine whether the functions are even, odd, or neither. 16.... Problem 17PT: For the following exercises, determine whether the functions are even, odd, or neither. 17. f(x)=1x Problem 18PT: For the following exercises, determine whether the functions are even, odd, or neither. 18. Graph... Problem 19PT: For the following exercises, find the inverse of the function Problem 20PT: For the following exercises, find the inverse of the function 20. f(x)=4x+7 Problem 21PT: For the following exercises, use the graph of g shown in Figure 1. On what intervals is the function... Problem 22PT: For the following exercises, use the graph of g shown in Figure 1. On what intervals is the function... Problem 23PT: For the following exercises, use the graph of g shown in Figure 1. 23. Approximate the local minimum... Problem 24PT: For the following exercises, use the graph of g shown in Figure 1. 24. Approximate the local maximum... Problem 25PT: For the following exercises, use the graph of the piecewise function shown in Figure 2. 25. Find... Problem 26PT: For the following exercises, use the graph of the piecewise function shown in Figure 2. 26. Find... Problem 27PT: For the following exercises, use the graph of the piecewise function shown in Figure 2. 27. Write an... Problem 28PT: For the following exercises, use the values listed Table 1. 28. Find F(6) . Problem 29PT: For the following exercises, use the values listed in Table 1. 29. Solve the equation F(x)=5 . Problem 30PT: For the following exercises, use the values listed in Table 1. 30. Is the graph increasing or... Problem 31PT: For the following exercises, use the values listed in Table 1. 31. Is the function represented by... Problem 32PT: For the following exercises, use the values listed in Table 1. 32. Find F1(15) . Problem 33PT: For the following exercises, use the values listed in Table 1 33. Given f(x)=2x+11 , find f1(x) . Problem 31RE: For the following exercises, use the graphs to determine the intervals on which the functions are...
Related questions
For the following function. Use algebra to find all critical and inflection points. Use algebra to identify local and global maxima and minima f in the interval. Use your graphical calculator or Desmos to confirm your answer
f (x ) = x 3 - 3x 2 (-1 ≤ x ≤ 3)
Definition Definition Highest point, either on the entire domain or on the given range of a function. The plural form of 'maximum' is 'maxima'.
Expert Solution
Given function is
f x = x 3 - 3 x 2 - 1 ≤ x ≤ 3
Step 2: To find the critical points f x = x 3 - 3 x 2
Differentiate with respect to x,
f ' x = 3 x 2 - 6 x
To find the critical points, take f ' x = 0
3 x 2 - 6 x = 0 3 x x - 2 = 0 3 x = 0 o r x - 2 = 0 x = 0 o r x = 2
As it is polynomial function, the domain of f x - ∞ , ∞
Also, 0 , 2 ∈ - ∞ , ∞ and 0 , 2 ∈ - 1 , 3
Hence, the critical points are x = - 1 , 0 , 2 , 3
f ' x = 3 x 2 - 6 x
Differentiate f ' x f x
f ' ' x = 6 x - 6 = 6 x - 1
Critical point
Value of f ' ' x
Maximum/Minimum
x = 0 f ' ' 0 = 6 0 - 6 = - 6 < 0 So, is local maximum.
x = 2 f ' ' 2 = 6 2 - 6 = 12 - 6 = 6 > 0 So, is local minimum.
x = 3 f ' ' 2 = 6 3 - 6 = 18 - 6 = 12 > 0 So, is global minimum.
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