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Question Use the table to answer the question. x y 0 −5 1 −9 2 −13 3 −17 Which of the following equations correctly describes the function in the table using function notation? (1 point) Responses f(x)=−5x−4 f of x is equal to negative 5 x minus 4 f(x)=−4x−5 f left parenthesis x right parenthesis equals negative 4 x minus 5 f(y)=−5x−4 f left parenthesis y right parenthesis equals negative 5 x minus 4 f(y)=−4x−5 f left parenthesis y right parenthesis equals negative 4 x minus 5 Skip to navigation

1 answer

To find the equation that describes the function in the table, let's analyze the data points provided:

  • When \( x = 0 \), \( y = -5 \)
  • When \( x = 1 \), \( y = -9 \)
  • When \( x = 2 \), \( y = -13 \)
  • When \( x = 3 \), \( y = -17 \)

Looking for a linear equation in the form \( y = mx + b \):

  1. Calculate the slope \( m \): \[ m = \frac{\Delta y}{\Delta x} = \frac{-9 - (-5)}{1 - 0} = \frac{-4}{1} = -4 \]

  2. Using \( m = -4 \), we can find \( b \) (the y-intercept) by substituting one of the points (e.g., \( x = 0, y = -5 \)): \[ y = -4(0) + b \implies -5 = b \] Thus, the equation becomes: \[ y = -4x - 5 \]

Now we can replace \( y \) with \( f(x) \): \[ f(x) = -4x - 5 \]

Therefore, the correct equation that describes the function in the table using function notation is: \[ f(x) = -4x - 5 \]

The correct response is: f(x) = −4x − 5