Answer:
Exponential functions are one of the most important functions in mathematics. Exponential functions have
many scientific applications, such as population growth and radioactive decay. Exponential function are also
used in finance, so if you have a credit card, bank account, car loan, or home loan it is important to
understand exponential functions and how they work.
Exponential functions are function where the variable x is in the exponent. Some examples of exponential
functions are f(x) = 2 x
, f(x) = 5 x – 2
, or f(x) = 9 2x + 1
. In each of the three examples the variable x is in the
exponent, which makes each of the examples exponential functions.
Graphing Exponential Functions
To begin graphing exponential functions we will start with two examples. We will graph the two
exponential functions by making a table of values and plotting the points. After graphing the first two
examples we will take a look at the similarities and differences between the two graphs. When creating a table of values, I always suggest starting with the numbers x = –2, –1, 0, 1, and 2 because it
is important to have different types of numbers, some negative, some positive, and zero.
Example 1: Graph f(x) = 2 x
.
x x
f(x) = 2
–2 2
2
1 1
f( 2) 2
2 4
- - = = =
–1 1
1
1 1
f( 1) 2
2 2
- - = = =
0 0
f(0) = 2 = 1
1 1
f(1) = 2 = 2
2 2
f(2) = 2 = 4
By plotting the five points in the table above and connecting the points, we get the graph shown above.
Notice that as the xvalues get smaller, x = –1, –2, etc. the graph of the function gets closer and closer to the
xaxis, but never touches the xaxis. This means that there is a horizontal asymptote at the xaxis or y = 0. A
horizontal asymptote is a horizontal line that the graph gets closer and closer to.
Step-by-step explanation:
