Graphing Exponential Functions What you need to know… To find the y-intercept of an exponential...
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Graphing Exponential Functions ~adapted from Walch Education
Graphing Exponential Functions What you need to know… To find the y-intercept of an exponential function, evaluate f(0). The y-intercept has the coordinates
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).
Slide 4
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) = ab x is
always the x-axis, or y = 0. If the exponential function is of the
form f(x) = ab x + k, then the function will be shifted vertically
by the same number of units as k.
Slide 5
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.
Slide 6
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.
Slide 7
Create a table of values. Choose values of x and solve for the
corresponding values of f(x).
Slide 8
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
Slide 9
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).
Slide 10
Graph the function. Use the table of values to create a graph
of the function
Slide 11
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.