2.14.2 Drawing a graph without using a calculator
To draw a graph without using a calculator
Substitute \( x \)-values into the given function to get \( y \) for each \( x \)
Use BODMAS/BIDMAS to find values of \( y \) for each \( x \)
Plot points and join with smooth curve instead of
Check your calculations for any points that do not appear to fit with the shape of the rest of the curve
Worked example:
The table shows some values of \( y=\frac{x^2}{2}+\frac{1}{x^2}-\frac{2}{x} \) , \( x≠0 \).
Complete the table.
Substitute the given \( x \) values into the equation to work out the \( y \) values.
\( x=-1 \):
\( y=\frac{(-1)^2}{2}+\frac{1}{(-1)^2}-\frac{2}{(-1)} \)
\( y=\frac{1}{2}+1+2 \)
\( y=3.5 \)
\( x=0.2 \):
\( y=\frac{(0.2)^2}{2}+\frac{1}{(0.2)^2}-\frac{2}{0.2} \)
\( y=\frac{0.04}{2}+\frac{1}{0.04}-10 \)
\( y=15.02 \)
\( y=15.0 \)
\( x=3 \)
\( y=\frac{3^2}{2}+\frac{1}{3^2}-\frac{2}{3} \)
\( y=\frac{9}{2}+\frac{1}{9}-\frac{2}{3} \)
\( y=3.94444… \)
\( y=3.9 \)
On the grid, draw the graph of \( y=\frac{x^2}{2}+\frac{1}{x^2}-\frac{2}{x} \) for \( -3≤x≤-0.3 \) and \( 0.2≤x≤3 \).
Plot the \( x \) and \( y \) coordinates from the table on to the grid.
Draw a smooth curve from the points.
The two parts of the curve should not be connected across the \( y \) axis.
