End of chapter exercises

\(x\)	−3	−2	−1	0	1	2	3
\(y\)

Complete the table of values for the equation \(y = -2x\).
Plot the ordered pairs on the Cartesian plane.
Draw the straight-line graph.
Is the graph increasing or decreasing?

\[y = -2x\]

\(x\)	−3	−2	−1	0	1	2	3
\(y\)	6	4	2	0	−2	−4	−6

and 3.
Decreasing

\(x\)	−3	−2	−1	0	1	2	3
\(y\)

Complete the table of values for the equation \(y = x^2 − 3\).
Plot the ordered pairs on the Cartesian plane.
Draw the curve.
Describe some of the features of the curve.
Does the point \((-5; 22)\) lie on the curve? Use a calculation in your answer.

\[y = x^2 − 3\]

\(x\)	−3	−2	−1	0	1	2	3
\(y\)	6	1	−2	−3	−2	1	6

and 3.
Turning point at \((0; -3)\). Minimum point \((0; -3)\). Symmetrical about the \(y\)-axis.
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.

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

Continuous
and 3.

Chapter summary

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