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End of chapter exercises

End of chapter exercises

\(x\) −3 −2 −1 0 1 2 3
\(y\)              
  1. Complete the table of values for the equation \(y = -2x\).
  2. Plot the ordered pairs on the Cartesian plane.
  3. Draw the straight-line graph.
  4. Is the graph increasing or decreasing?
  1. \[y = -2x\]
\(x\) −3 −2 −1 0 1 2 3
\(y\) 6 4 2 0 −2 −4 −6
  1. and 3.
  2. Decreasing
\(x\) −3 −2 −1 0 1 2 3
\(y\)              
  1. Complete the table of values for the equation \(y = x^2 − 3\).
  2. Plot the ordered pairs on the Cartesian plane.
  3. Draw the curve.
  4. Describe some of the features of the curve.
  5. Does the point \((-5; 22)\) lie on the curve? Use a calculation in your answer.
  1. \[y = x^2 − 3\]
\(x\) −3 −2 −1 0 1 2 3
\(y\) 6 1 −2 −3 −2 1 6
  1. and 3.
  2. Turning point at \((0; -3)\). Minimum point \((0; -3)\). Symmetrical about the \(y\)-axis.
  3. For \(x = -5\), \(y = (-5)^2 − 3 = 25 − 3 = 22\)
    Yes, the point \((-5; 22)\) lies on the curve.

A car travels at a constant speed of \(120 \text{ km}{\cdot}\text{h}^{-1}\) for 9 minutes. Over the next 2 minutes, it reduces its speed at a steady rate until it reaches a speed of \(60 \text{ km}{\cdot}\text{h}^{-1}\). The car travels at \(60 \text{ km}{\cdot}\text{h}^{-1}\) for 4 minutes. Over the next 1 minute, it reduces its speed at a steady rate and comes to a complete stop.

  1. Is the data in this situation discrete or continuous?
  2. Use the information provided to draw a suitable graph.
  3. On your graph indicate the sections where the graph is decreasing and constant.
  1. Continuous
  2. and 3.