How Do You Graph the Natural Base Exponential Function?

f(x) = e^x is the natural base exponential function
'e' is the natural base
'≈' means 'approximately equal to'
Plug each 'x' value into e^x
You can either use the 'e' button on your calculator or use the approximation 2.718 for 'e' to find each value
f(x) = e^x has a horizontal asymptote along the x-axis
An asymptote is an imaginary line that a graph approaches but never reaches

1. We can choose some values for 'x' to plug into f(x) = e^x to find points to graph
2. Remember, our variable here is 'x', NOT 'e'
3. 'e' is the natural base and is approximately equal to 2.718 -- it is NOT a variable
1. Remember, our function is the natural base exponential function f(x) = e^x
2. So we need to choose some values for 'x' that we can plug into e^x to get values for f(x)
1. If you press the e^x button on your calculator and then enter each value for 'x', it will approximate those values for you
2. Remember, we know that 'e' is approximately equal to 2.718
3. So you could also use 2.718 in place of 'e' to get an approximation
1. Now that we have values for x and f(x), we can plot points in order to graph our function
1. Remember, f(x) is the same thing as y
2. So we can turn each pair of x and f(x) values into an ordered pair and plot them in the coordinate plane
3. Plot the points (-2,0.135), (-1,0.368), (0,1), (1,2.718), and (2,7.389)
4. Connecting the points gives us the graph of our exponential function
1. Notice how the graph looks like it gets really close to the x-axis, but never actually touches it
2. The x-axis is where y = 0
1. An asymptote is an imaginary line that a graph approaches but never reaches
2. As our x-values get more and more negative, our f(x) values will get closer and closer to 0, but will never actually reach 0

Graph f(x) = ex by making a table.