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MAC2311 Lecture 1: 1.1 Functions and their Representations Notes

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20 Dec 2017

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Miami Dade College

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Mathematics: Calculus & Pre-Calculus

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1. 1 functions and their representations notes: sterling. Provide a generalization to each of the key terms listed in this section. Functions are relations between a set of inputs (x-values) and a set of outputs (y-values). Domains are general sets of all of the x-coordinates, which are the rst half of the elements of any ordered pair. Ranges are general sets of all of the y-coordinates, which are the second half of the elements of any ordered pair. The variable x since it can be assigned any number(s) from the given domain. The variable y since its own value is depending on x. This method occurs when you are given the function itself like f (x) = 2x + 5. This method occurs when you are describing the function in words like [ ve plus twice the original value]. This method (best) occurs when you are creating a table with some of the function"s points.

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Related Questions

Algebra

The function f(x) = 4x/9x-7 is one-to-one. Find its inverse and check your answer. f -1 (x) = (Simplify your answer.) Graph the function. Based on the graph, state the domain and the range and find any intercepts. The domain is . (Type your answer in interval notation.) The range is . (Type your answer in interval notation.) Find the intercepts, if there are any. Select the correct choice below and fill in any answer boxes within your choice. The intercept(s) is'are . (Type an ordered pair. Use a comma to separate answers as needed. Type an exact answer.) Solve the equation. What is the solution? x = (Use a comma to separate answers.) If f(x) = 5x2 + 3 and g(x) = 9x + a, find a so that the graph of f g crosses the y-axis at 8. What is the value of a? a = (Use reduced fractions or integers. Use commas to separate values.) The function f(x) = 7/4+x is one-to-one. Find its inverse and check your answer. f -1 (x) = (Simplify your answer.) Suppose that H(x) = (1/4)x - 4096 What is H( - 5)? What is the point that corresponds to this vahie on the graph of H? If H(x) = - 4032, what is x? What is the point that corresponds to this vahie on the graph of H? Find the zero of H. H( - 5) = (Type an integer or a simplified fraction.) The point that corresponds to this vahie on the graph of H is . (Type an ordered pair, but do not use commas in any individual coordinates.) If H(x) = - 4032, then x = . (Type an integer or a simplified fraction.) The point that corresponds to this vahie on the graph of H is . (Type an ordered pair, but do not use commas in any individual coordinates.) The zero of H is x = (Type an integer or a simplified fraction.) If f(x) = x3 - 3x2 + 2x - 9 and g(x) = 4: find (f g)(x) and (g f)(x). What is (f g)(x)? What is (f g)(x)? (f g)(x) = What is (g f)(x)? (g f)(x) = The function f(x) = 8x/x+5 is one-to-one. Find its inverse and check your answer. f -1 (x) = (Simplify your answer.) Solve the equation. ex= e9x + 72 x = (Use a comma to separate answers as needed.)

Show transcribed image text The function f(x) = 4x/9x-7 is one-to-one. Find its inverse and check your answer. f -1 (x) = (Simplify your answer.) Graph the function. Based on the graph, state the domain and the range and find any intercepts. The domain is . (Type your answer in interval notation.) The range is . (Type your answer in interval notation.) Find the intercepts, if there are any. Select the correct choice below and fill in any answer boxes within your choice. The intercept(s) is'are . (Type an ordered pair. Use a comma to separate answers as needed. Type an exact answer.) Solve the equation. What is the solution? x = (Use a comma to separate answers.) If f(x) = 5x2 + 3 and g(x) = 9x + a, find a so that the graph of f g crosses the y-axis at 8. What is the value of a? a = (Use reduced fractions or integers. Use commas to separate values.) The function f(x) = 7/4+x is one-to-one. Find its inverse and check your answer. f -1 (x) = (Simplify your answer.) Suppose that H(x) = (1/4)x - 4096 What is H( - 5)? What is the point that corresponds to this vahie on the graph of H? If H(x) = - 4032, what is x? What is the point that corresponds to this vahie on the graph of H? Find the zero of H. H( - 5) = (Type an integer or a simplified fraction.) The point that corresponds to this vahie on the graph of H is . (Type an ordered pair, but do not use commas in any individual coordinates.) If H(x) = - 4032, then x = . (Type an integer or a simplified fraction.) The point that corresponds to this vahie on the graph of H is . (Type an ordered pair, but do not use commas in any individual coordinates.) The zero of H is x = (Type an integer or a simplified fraction.) If f(x) = x3 - 3x2 + 2x - 9 and g(x) = 4: find (f g)(x) and (g f)(x). What is (f g)(x)? What is (f g)(x)? (f g)(x) = What is (g f)(x)? (g f)(x) = The function f(x) = 8x/x+5 is one-to-one. Find its inverse and check your answer. f -1 (x) = (Simplify your answer.) Solve the equation. ex= e9x + 72 x = (Use a comma to separate answers as needed.)

Algebra

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