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