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3 Look again at Practice Exercise 3 and its solution from Chap 27 Create a table of values for both functions, based on x-values of 3, 2, 1, 0, 1, 2, 3, and 4 Here are the functions that came from the original equations: y = 3x + 1

This f is a function because every person has one and only one legal name Notice that several people may have the same name (such as Jack Armstrong), but that is allowed in the definition of function

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and y = 2x 2 3x + 3 Use bold numerals to indicate the real solutions, if any exist 4 Plot an approximate graph showing the curves based on the table you created when you worked out Prob 3 On the x axis, let each increment represent 1 unit On the y axis, let each increment represent 5 units Draw the first function s graph as a solid line or curve Draw the second function s graph as a dashed line or curve Plot and label all real solution points, if any exist 5 Look again at Practice Exercise 5 and its solution from Chap 27 Create a table of values for both functions, based on x-values of 4, 3, 2, 1, 0, 1, 2, 3, and 4 Here are the functions that came from the original equations: y = x2 + x + 1 and y = x 2 2x 2 Use bold numerals to indicate the real solutions, if any exist 6 Plot an approximate graph showing the curves based on the table you created when you worked out Prob 5 On the x axis, let each increment represent 1 unit On the y axis, let each increment represent 4 units Draw the first function s graph as a solid line or curve Draw the second function s graph as a dashed line or curve Plot and label all real solution points, if any exist 7 Look again at Practice Exercise 7 and its solution from Chap 27 Create a table of values for both functions, based on x-values of 3, 2, 1, 0, 1, 2, and 3 Here are the functions that came from the original equations: y = x 2 and y = 2x 3 Use bold numerals to indicate the real solutions, if any exist 8 Plot an approximate graph showing the curves based on the table you created when you worked out Prob 7 On the x axis, let each increment represent 1/2 unit On the y axis, let each increment represent 10 units Draw the first function s graph as a solid line or curve Draw the second function s graph as a dashed line or curve Plot and label all real solution points, if any exist.

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In calculus, the set S (called the domain of the function) and the set T (called the range of the function) will usually be sets of numbers; in fact they will often consist of one or more intervals in R The rule f will usually be given by one or more formulas Many times the domain and range will not be given explicitly These ideas will be illustrated in the examples below

9 Look again at Practice Exercise 9 and its solution from Chap 27 Create a table of values for both functions, based on x-values of 3, 2, 1, 0, 1, 2, 3, and 4 Here are the functions that came from the original equations: y = 2x 3 + x 2 + x 4 and y = 3x 3 2x 2 + 4x 5 Use bold numerals to indicate the real solutions, if any exist 10 Plot an approximate graph showing the curves based on the table you created when you worked out Prob 9 On the x axis, let each increment represent 1 unit On the y axis, let each increment represent 20 units Draw the first function s graph as a solid line or curve Draw the second function s graph as a dashed line or curve Plot and label all real solution points, if any exist

Logarithms and exponentials show up in many branches of mathematics, sometimes unexpectedly If you re getting ready for more advanced subjects such as analysis, calculus, or engineering mathematics, you should know something about logarithms and exponentials

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