Graphing
Exponential
Functions
~adapted from Walch Education
What you need to know…
• To find the y-intercept of an exponential function, evaluate f(0).
• The y-intercept has the coordinates (0, f(0)).
• To locate the y-intercept of a graphed function, determine the coordinates of the function where the line crosses the y-axis.
• To find the x-intercept in function notation, set f(x) = 0 and solve for x.
• The x-intercept has the coordinates (x, 0).
What else?
• To locate the x-intercept of a graphed function, determine the coordinates of the line where the line crosses the x-axis.
• Not all exponential functions cross the x-axis.
• The asymptote of exponential functions of the form f(x) = abx is always the x-axis, or y = 0.
• If the exponential function is of the form f(x) = abx + k, then the function will be shifted vertically by the same number of units as k.
And…
• The asymptote is then y = k.
• The end behavior, or the behavior of the graph as x becomes larger or smaller, will always be one of three descriptions: infinity, negative infinity, or the asymptote.
• It is easiest to first graph the function and then observe what happens to the value of y as the value of x increases and decreases.
• Graph complex exponential models using technology as values can become quite large or small very quickly.
Practice
Create a table of values for the
exponential function f(x) = –1(3)x – 2.
Identify the asymptote and y-intercept
of the function. Plot the points and
sketch the graph of the function, and
describe the end behavior.
Create a table of values.
Choose values of x and solve for the
corresponding values of f(x).
Identify the asymptote of the function
• In the function f(x) = –1(3)x – 2, the
value of k is –2.
The asymptote of the function is y = –2
The asymptote of the function is always the
constant, k
Determine the y-intercept of the function
• The y-intercept of the function is the
value of f(x) when x is equal to 0.
• It can be seen in the table that when x
= 0, f(x) = –3.
The y-intercept is (0, –3).
Graph the function.
Use the table of
values to
create a graph of the
function
Describe the end behavior of the graph.
• The end behavior is what happens at
the ends of the graph.
• As x becomes larger, the value of the
function approaches negative infinity.
• As x becomes smaller, the value of the
function approaches the asymptote, –
2.
THANKS FOR WATCHING!
~DR. DAMBREVILLE