A-level Mathematics/Edexcel/Core 1/Graphs and transformations

Graphs

For C1 it is important to be able to draw graphs and labelling points of intersection between graphs, as well as axes intersection points i.e., where the graph crosses the x-axis and the y-axis. You must be familiar with the equation y = mx + c which is the equation for any straight line graph. For drawing a line graph, you must be able to put any linear equation into the above form and work out the gradient (m) and the y-intercept (+c) For example, the line y + x = 7, we must put it into the y = mx + c form, so we get y = -x + 7. From here we can see that the gradient is -1 and the line crosses the y axis at 7. We can substitute in anotehr x value, say 1, to get another y value (-1 + 7 = 6) so we have a gradient, -1, a y-intercept = 7, and a co-ordinate (-1,6) so now we can draw the line. To draw a quadratic graph, we must be familiar with factorizing (see relevant page) and from here we get the roots of the graph. The general shape for a quadratic is the parabola which is a U shape for a positive quadratic, and an upside-down U shape for a negative one. We can substitiue x = 0 into the equation of the quadratic to get the y-interecept.

Transformations

There are 4 basic types of transformations y = f(x)+a - movement up by a units y = f(x-a) - movement along by a units (for f(x+a) it would be a movement along by -a units) y = af(x) - a vertical stretch of sf a y = f(ax) - a horizontal stretch of sf 1/a