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3. Graphs Example 1


Describe the shape of the following lines: (a) y = x . . . . . . . . . . . . . . . . . . . . straight line (b) y = x2


(c) y = 3x . . . . . . . . . . . . . . . . . . . straight line (d) y2


(e) y = x3


. . . . . . . . . . . . . . . . . . . . curve, one bend


= x . . . . . . . . . . . . . . . . . . . . curve, one bend –3x2


(f) y = 10x – 2 . . . . . . . . . . . . . . . straight line (g) y = 4x2 (h) y = x4 (i) y = x4 (j) y = x3


–5x3 + x3 + x2


RULE Rule for drawing graphs:


First we need to collect a number of points to plot, to see what shape the graph has:


1. Write down the value of x from –3 to +3 on top of the chart. 2. Write down the equation on the side of the chart. 3. Values of y can be calculated by putting values of x into the equation and adding.


4. Each value of x now has a corresponding value for y which may be plotted.


+ x2


+ x + 3 . . . . . . . . . . . . . curve, one bend + 5x2


– x + 3 . . . . . . . . . curve, two bends


+ 4x – 4 . . . . curve, three bends + x + 3 . . . . . . . curve, three bends + x + 2 . . . . . . . . . . curve, two bends


Example 2 x


2x 3 y


Draw the line y = 2x + 3. Use the value of x from –3 to +3.


–3 –6 3


–3


–2 –4 3


–1


–1 –2 3 1


y


0 0 3 3


1 2 3 5


2 4 3 7


3 6 3 9


x


37


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