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Lesson 6: Sketch Functions From Verbal Descriptions — Practice Questions

  1. 1. A sprinter begins a race from a standstill, accelerating rapidly. Which option best describes the graph of the distance she has run versus time during this initial acceleration?

    • A. A straight line with a positive slope
    • B. An upward curve that gets steeper
    • C. An upward curve that gets flatter
    • D. A horizontal line
  2. 2. A hot soup is left on a table to cool. Its temperature decreases quickly at first, and then more slowly as it approaches room temperature. What does the temperature vs. time graph look like?

    • A. A downward curve that gets flatter
    • B. A downward curve that gets steeper
    • C. A straight line with a negative slope
    • D. An upward curve that gets flatter
  3. 3. On a graph of a quantity versus time, a curve that becomes progressively ___ indicates that the rate of change is increasing.

  4. 4. A factory's total production increases over the day, but the rate of production slows down near closing time. Which graph represents the total items produced versus time?

    • A. A straight line with a positive slope
    • B. An upward curve that gets steeper
    • C. An upward curve that gets flatter
    • D. A downward curve that gets flatter
  5. 5. A streaming plan's monthly cost, $c$, depends on the number of screens, $s$, allowed. In this relationship, the number of screens, $s$, is the ___ variable. (enter "independent" or "dependent")

  6. 6. The remaining battery percentage, $p$, of a smartphone is affected by the hours of video playback, $h$. Which variable is the dependent variable in this situation?

    • A. The remaining battery percentage, $p$.
    • B. The hours of video playback, $h$.
    • C. Both $p$ and $h$.
    • D. Neither $p$ nor $h$.
  7. 7. The total time, $T$, it takes to fill a swimming pool depends on the pool's volume, $V$, and the flow rate of the hose, $R$. The pool's volume, $V$, is an ___ variable. (enter "independent" or "dependent")

  8. 8. A chef notes the final temperature of a soup, $T$, depends on how many minutes it simmers, $m$. A student argues that $m$ is dependent because the chef chooses $m$ based on the target $T$. Which statement is true?

    • A. The simmering time, $m$, is the dependent variable because the chef chooses it.
    • B. The soup's temperature, $T$, is the independent variable because it's the goal.
    • C. The simmering time, $m$, is the independent variable because it causes the temperature to change.
    • D. Both $T$ and $m$ are independent variables.
  9. 9. The resale value of a textbook, $v$, decreases based on its age in years, $y$. In this relationship, the resale value, $v$, is the ___ variable. (enter "independent" or "dependent")