Mastering Integration
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Questions and Answers

Which of the following represents the relationship between the input and the output on a graph?

  • The position on the x-axis represents the input and the position on the y-axis represents the output. (correct)
  • The position on the y-axis represents the input and the position on the y-axis represents the output.
  • The position on the y-axis represents the input and the position on the x-axis represents the output.
  • The position on the x-axis represents the input and the position on the x-axis represents the output.

    • What formula is used to calculate the distance between two points on a graph?

  • $D = \frac{y_2 - y_1},{x_2 - x_1}$ (correct)
  • $D = y_2 - y_1 \div x_2 - x_1$
  • $D = \frac{y_2},{y_1} \div \frac{x_2},{x_1}$
  • $D = \Delta y \div \Delta x$

    • What is the derivative of the function $f(x) = y$?

  • The distance between two points on the graph.
  • The difference between the initial and final positions on the graph.
  • The formula $D = \frac{y_2 - y_1},{x_2 - x_1}$.
  • The rate of change in the y-axis when the rate of change in the x-axis is infinitely small. (correct)

    • In the equation $D = \frac{f(b) - f(a)},{b - a}$, what does $D$ represent?

    <p>The distance between the initial and final positions on the graph.</p> Signup and view all the answers

    What is the distance between two points on a graph if $f(b) = 5$, $f(a) = 2$, $b = 4$, and $a = 1$?

    <p>$D = \frac{5 - 2},{4 - 1}$</p> Signup and view all the answers

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