Page 742 - Algebra 1

L E S S O N Identifying and Graphing Exponential
108
Functions
Warm Up
NewConcepts
1. Vocabulary In the expression 35, 5 is the . (3)
Simplify. 2. 42
(3)
4. 2 · 5-2 (3)
3. 6-3 (3)
5. 5 · 2-1 (3)
Exponential Function
An exponential function is a function of the form f(x) = abx, where a and b are nonzero constants and b is a positive number not equal to 1.
Reading Math
The value of b in an exponential function is comparable to r in a geometric sequence.
Example
1
Hint
a-n = _1n a
Online Connection www.SaxonMathResources.com
Inageometricsequence,anyterm,exceptthefirst,canbefoundbymultiplying the previous term by the common ratio. In the geometric sequence 2, 6, 18, 54, 162, ..., the common ratio is 3.
The sequence can also be written like this: 2, 2(3)1, 2(3)2, 2(3)3, 2(3)4, .... Or, with a1 representing the first term and r representing the common ratio, it can be written as a1, a1(r)1, a1(r)2, a1(r)3, a1(r)4, ....
Using n as the term number, observe that the nth term of a geometric sequence can be found by using the rule an = a1rn-1.
Notice that the independent variable n occurs in the exponent of the function rule. Any function for which the independent variable is an exponent is an exponential function.
Evaluating an Exponential Function
Evaluate each function for the given values.
a. f(x) = 5x for x = -3, 0, and 4. SOLUTION
Use the order of operations.
f(-3)=5-3 =_1 =_1 , f(0)=50 =1, f(4)=54 =625 53 125
b. f(x) = 2(4)x for x = -1, 1, and 2.
SOLUTION
Use the order of operations. Evaluate exponents before multiplying.
f(-1)=2(4)-1 =2·_1 =_2 =_1 442
f(1)=2(4)1 =2(4)=8
f (2) = 2(4)2 = 2(16) = 32
Lesson 108 727