How to graph exponential functions?


Quick Answer

To graph exponential functions, create a table of values first, calculating the values for f(x) according to the function given. Each pair of numbers constitutes the coordinates for the points to be drawn on the graph. X will give a coordinate for the x-axis, and f(x) is the coordinate for the y-axis.

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Full Answer

Equations for exponential functions have this form: f(x) equals a to the power of x. Exponential functions describe a mathematical procedure whereby a number is multiplied by another number continually.

  1. Create a table of values
  2. Draw a table with two columns and as many rows as the number of points needed for the graph. At the top of the left column put x, and at the top of the right column put f(x), which is another way of saying "y". In the first cell of the left column put "-2", put "-1" in the cell below it, and 0, 1 and 2 in the following cells. Calculate the value of f(x) according to the function and put these values in the "f(x)" column. For the function: f(x) equals 3 to the power of x, the f(x) value corresponding to the first cell in the left column, "-2", is 1/9, because 3 to the power of -2 equals 1/9. The rest of the values for the right column are: 1/3, 1, 3 and 9.

  3. Draw the graph
  4. Draw two axes: x is a horizontal one and y is vertical. They cross at 0. Plot the points from the value table onto the graph. For the first pair: x=-2 and f(x)=1/9, put a dot in the left upper quadrant of the graph, above -2 on the x-axis and to the left of 1/9 on the y-axis. Continue for the rest of the pairs. Connect the dots.

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