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Questions and Answers
Which of the following represents the cost of hiring guides as a function of the number of tourists who wish to explore the cave?
Which of the following represents the cost of hiring guides as a function of the number of tourists who wish to explore the cave?
Which of the following represents the cost of renting a videoke machine as a piecewise function of the number of days it is rented?
Which of the following represents the cost of renting a videoke machine as a piecewise function of the number of days it is rented?
What is the simplified form of (f + g)(x)?
What is the simplified form of (f + g)(x)?
What is the simplified form of (f * g)(x)?
What is the simplified form of (f * g)(x)?
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What is the simplified form of (f∘g)(x)?
What is the simplified form of (f∘g)(x)?
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Which of the following best represents the function (f - g)(x)?
Which of the following best represents the function (f - g)(x)?
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Which of the following best represents the function (f * g)(x)?
Which of the following best represents the function (f * g)(x)?
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Which of the following best represents the function (g/f)(x)?
Which of the following best represents the function (g/f)(x)?
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Which of the following best represents the function (f∘g)(x)?
Which of the following best represents the function (f∘g)(x)?
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Which of the following best represents the function (g∘g)(x)?
Which of the following best represents the function (g∘g)(x)?
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Which of the following best represents the function (f + g)(x)?
Which of the following best represents the function (f + g)(x)?
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What is the simplified form of (f/g)(x)?
What is the simplified form of (f/g)(x)?
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Which of the following best represents the function (g∘f)(x)?
Which of the following best represents the function (g∘f)(x)?
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What is the simplified form of (f∘f)(x)?
What is the simplified form of (f∘f)(x)?
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Which of the following represents the cost of renting a videoke machine as a piecewise function of the number of days it is rented?
Which of the following represents the cost of renting a videoke machine as a piecewise function of the number of days it is rented?
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Which of the following best describes a rational function?
Which of the following best describes a rational function?
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Which of the following is true about the domain of a rational function?
Which of the following is true about the domain of a rational function?
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Which of the following best describes an asymptote?
Which of the following best describes an asymptote?
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What is the x-intercept of the rational function f(x) = (x-4)/(x-2)?
What is the x-intercept of the rational function f(x) = (x-4)/(x-2)?
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What is the y-intercept of the rational function f(x) = (x-4)/(x-2)?
What is the y-intercept of the rational function f(x) = (x-4)/(x-2)?
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Which of the following best describes a rational function?
Which of the following best describes a rational function?
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What is the domain of a rational function?
What is the domain of a rational function?
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What is the y-intercept of the rational function $f(x) = \frac{x-4}{x-2}$?
What is the y-intercept of the rational function $f(x) = \frac{x-4}{x-2}$?
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What is the x-intercept of the rational function $f(x) = \frac{x-4}{x-2}$?
What is the x-intercept of the rational function $f(x) = \frac{x-4}{x-2}$?
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What is an asymptote in a rational function?
What is an asymptote in a rational function?
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Which of the following best describes a rational function?
Which of the following best describes a rational function?
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What is the domain of a rational function?
What is the domain of a rational function?
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What is an asymptote in a rational function?
What is an asymptote in a rational function?
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What is the x-intercept of the rational function $f(x) = rac{x-4}{x-2}$?
What is the x-intercept of the rational function $f(x) = rac{x-4}{x-2}$?
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What is the y-intercept of the rational function $f(x) = rac{x-4}{x-2}$?
What is the y-intercept of the rational function $f(x) = rac{x-4}{x-2}$?
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Which of the following best describes an inverse function?
Which of the following best describes an inverse function?
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Which of the following is the correct equation to find the inverse of a function f(x)?
Which of the following is the correct equation to find the inverse of a function f(x)?
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Which of the following is the correct equation to determine if g is the inverse of f?
Which of the following is the correct equation to determine if g is the inverse of f?
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What is the inverse of the function f(x) = x - 2?
What is the inverse of the function f(x) = x - 2?
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Which of the following is true about the domain and range of a function and its inverse?
Which of the following is true about the domain and range of a function and its inverse?
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Which of the following functions is the inverse of $f(x) = x^2 - 2x + 3$?
Which of the following functions is the inverse of $f(x) = x^2 - 2x + 3$?
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Which of the following functions is the inverse of $f(x) = \frac{x-2},{x+2}$?
Which of the following functions is the inverse of $f(x) = \frac{x-2},{x+2}$?
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Which of the following functions is the inverse of $f(x) = x^2 + x$?
Which of the following functions is the inverse of $f(x) = x^2 + x$?
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Which of the following functions is the inverse of $f(x) = 1 - 4 - 3x$?
Which of the following functions is the inverse of $f(x) = 1 - 4 - 3x$?
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Which of the following functions is the inverse of $f(x) = x^2 - 2$?
Which of the following functions is the inverse of $f(x) = x^2 - 2$?
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Which of the following functions is the inverse of $f(x) = x^2 - 2x + 3$?
Which of the following functions is the inverse of $f(x) = x^2 - 2x + 3$?
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Which of the following functions is the inverse of $f(x) = 1 - 4 - 3x$?
Which of the following functions is the inverse of $f(x) = 1 - 4 - 3x$?
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Which of the following best describes a rational function?
Which of the following best describes a rational function?
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Which of the following represents the cost of hiring guides as a function of the number of tourists who wish to explore the cave?
Which of the following represents the cost of hiring guides as a function of the number of tourists who wish to explore the cave?
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What is the domain of a rational function?
What is the domain of a rational function?
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Study Notes
Functions and Their Operations
- The cost of hiring guides can be represented as a function of the number of tourists who wish to explore the cave.
- The cost of renting a videoke machine can be represented as a piecewise function of the number of days it is rented.
Composition of Functions
- The simplified form of (f + g)(x) represents the sum of two functions f and g.
- The simplified form of (f * g)(x) represents the product of two functions f and g.
- The simplified form of (f∘g)(x) represents the composition of two functions f and g.
Inverse Functions
- The inverse of a function f(x) is denoted as f^(-1)(x) and satisfies the equation f(f^(-1)(x)) = x.
- The correct equation to find the inverse of a function f is x = f(y).
- The correct equation to determine if g is the inverse of f is f(g(x)) = g(f(x)) = x.
- The inverse of a function switches the input and output values.
Rational Functions
- A rational function is a function that can be expressed as the ratio of two polynomials.
- The domain of a rational function is all real numbers except where the denominator is zero.
- An asymptote in a rational function is a line that the graph approaches as the input values increase or decrease without bound.
- The x-intercept of a rational function is the point where the graph crosses the x-axis.
- The y-intercept of a rational function is the point where the graph crosses the y-axis.
Examples of Functions
- The inverse of the function f(x) = x - 2 is f^(-1)(x) = x + 2.
- The inverse of the function f(x) = x^2 - 2x + 3 is a complex function.
- The inverse of the function f(x) = (x-2)/(x+2) is a complex function.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of evaluating functions by taking this quiz. Replace the variable in the function with a value from the domain and compute the result.