Home >> Science & Nature >> Science

How to Graph Exponents of X

Mathematical functions allow an input to be manipulated in order to generate an output. There are many important mathematical functions, including power functions such as x^n. A power function raises x to some power, and the power is signified by the exponent. The graph of x^n varies depending on the exponent. Generally, when n is even, the graph is a parabola that is symmetrical about the y axis.

Things You'll Need

Graph paper

Instructions

- 1
  Write down the equation that needs to be graphed. Functions with an exponent of x take the general form y = x^n. When n is 0, the graph is equal to 1 for all x, and when n is 1, y increases linearly with x. For all values of n above 1, a common trend follows. For even values of n, the graph is parabolic. For odd values of n, 3 and above, the graph looks like two half-parabolas pointing in opposite directions on the y-axis.
- 2
  Use the example: y = x^2.
  
  Make a table for the x and y values. Label the table headings "x" and "y = x^2."
  
  Plug in values for "x" and calculate the solutions for "y = x^2."
  
  Following the example:
  
  x....................y = x^2
  
  x = 0............. y = 0
  
  x = 1............. y = 1
  
  x = 2............ y = 4
  
  x = 3............ y = 9
- 3
  Draw the axes on the graph. Label the x-axis "x" and the y-axis "y = x^2". Find the x value for the first point, and find the corresponding y value. Put a cross where the x and y values intersect. Repeat this for all values in the table. Draw a slightly curving line between adjacent points. The graph is complete.

Science