Drawing Graphs Using a Table
How do I draw a graph using a table of values?
- To create a table of values
- substitute different x-values into the equation
- This gives the y-values
- To plot the points
- Use the x and y-values to mark crosses on the grid at the coordinates (x , y )
- Each point is expected to be plotted to an accuracy within half of the smallest square on the grid
- Draw a single smooth freehand curve
- Go through all the plotted points
- Make it the shape you would expect
- For example, quadratic curves have a vertical line of symmetry
- Do not use a ruler for curves!
Which numbers should I be careful with?
- For quadratic graphs, be careful substituting in negative numbers
- Always put brackets around them and use BIDMAS
- For example, x = -3 in y = -x2 + 8x
- becomes y = -(-3)2 + 8(-3)
- which simplifies to -9 - 24
- so y = - 33
- For example, x = -3 in y = -x2 + 8x
- For reciprocal graphs like , do not include x = 0
- You cannot divide by zero
- You get an error on your calculator
- There is no value at x = 0
- The L-shaped branches can't cross the y-axis
- An example is given below with
- You cannot divide by zero
-3 | -2 | -1 | 0 | 1 | 2 | 3 | |
No value |
How do I use the table function on my calculator?
- Calculators can create tables of values for you
- Find the table function
- Type in the graph equation (called the function, f(x))
- Use the alpha button then X or x
- Press = when finished
- If you are asked for another function, g(x), press = to ignore it
- Type in the graph equation (called the function, f(x))
- Enter the start value
- The first x-value in the table
- Press =
- Enter the end value
- The last x-value in the table
- Enter the step size
- How big the steps (gaps) are from one x-value to the next
- Press =
- Then scroll up and down to see all the y-values
Examiner Tip
- If you find a point that doesn't seem to fit the shape of the curve, check your working!
- If any y-values are given in the question, check that your calculations agrees with them.
Worked example
Start at -1.5, end at 1.5 and use steps of 0.5
On a non-calculator paper, substitute the x-values into the equation, for example x = -1.5
-8 | 8 | 10 | 8 | 2 |
Note the different scales on the axes