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📏honors pre-calculus review

Y = f(x)

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

The expression 'y = f(x)' represents a function, where 'y' is the dependent variable and 'x' is the independent variable. This notation indicates that the value of 'y' is determined by the value of 'x' through the function 'f'. The function 'f' is a rule or a relationship that maps each input value of 'x' to a unique output value of 'y'.

5 Must Know Facts For Your Next Test

  1. The expression 'y = f(x)' indicates that the value of 'y' is a function of the value of 'x'.
  2. The function 'f' maps each input value of 'x' to a unique output value of 'y'.
  3. The domain of the function 'f' is the set of all possible input values (x) for which the function is defined.
  4. The range of the function 'f' is the set of all possible output values (y) that the function can produce.
  5. Inverse functions, denoted as 'x = g(y)', are functions that undo the original function 'f(x)'.

Review Questions

  • Explain the relationship between the independent variable 'x' and the dependent variable 'y' in the expression 'y = f(x)'.
    • In the expression 'y = f(x)', the independent variable 'x' is the input value that determines the value of the dependent variable 'y' through the function 'f'. This means that for each value of 'x', the function 'f' will produce a unique corresponding value of 'y'. The value of 'y' is dependent on the value of 'x', and the function 'f' describes the relationship between these two variables.
  • Describe the concept of the domain and range of a function in the context of 'y = f(x)'.
    • The domain of the function 'f(x)' is the set of all possible input values (x) for which the function is defined. This means that the function must be able to produce a valid output value (y) for each input value (x) in the domain. The range of the function 'f(x)' is the set of all possible output values (y) that the function can produce. The domain and range are important characteristics of a function that describe the set of inputs and outputs that the function can handle.
  • Explain the relationship between a function 'f(x)' and its inverse function 'g(y)' in the context of the expression 'y = f(x)'.
    • The inverse function 'g(y)' is a function that undoes the original function 'f(x)'. In other words, if 'y = f(x)', then the inverse function 'g(y)' would satisfy the equation 'x = g(y)'. This means that the input and output values of the original function and its inverse function are reversed. The inverse function allows you to find the original input value 'x' given the output value 'y' of the original function 'f(x)'. Understanding the relationship between a function and its inverse is crucial for solving problems involving functions and their properties.

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