Exponential Function
Exponential Function
Exponential Function
General Mathematics
Lesson Objectives
At the end of the lesson, the students must be
able to:
• represent an exponential function through its:
(a) table of values, (b) graph, and (c) equation;
• find the domain and range of an exponential
function;
• find the intercept, zeros, and asymptote of an
exponential function; and
• graph exponential functions.
Zero as an Exponent
• If a ≠ 0, then a⁰ = 1
Illustration:
To evaluate 3⁰ ∙ 3², we have
3⁰ ∙ 3² = 3⁰⁺² = 3² = 9 or
3⁰ ∙ 3² = 1 ∙ 3² = 1 ∙ 9 = 9
Negative Exponent
• If n is any integer, and a and b are not equal to
zero, then
n n n
n 1 1 a b
a n and
a a b a
• Illustration
13 1
2 3
2 8
Note: The negative exponent does not make the
answer negative
Definition
Transformation – the process of moving a figure
from the starting position to some ending
position without changing its size and shape.
c. d.
Solution to Example 1
a. b.
c. d.
Example 2
Translate each shape in the direction indicated
by the arrow.
a. b.
Solution to Example 2
a. b.
Example 3
Translate each figure as indicated.
a. b.
Example 4
Perform a glide reflection on:
a. b.
Activity
The Exponent National High School with 1,500
population, including the teaching and non-
teaching staff, is located in one of the affected by
the earthquake. Due to recurrent aftershcocks,
everyone wants to know if classes are suspended.
The school principal makes a decision and sends
a text message to the assistant principal and to
the prefect of activities. These two members of
the community each sends the text message to
two members of the community, and so on.
This texting diagram can be represented by a
tree diagram that goes like this:
1. What do the smart phones of this tree diagram
represent? What do the segments represent?
Graph: x = 2ʸ.
Solution to Example 10
The Euler’s number e is called the natural
number. The function f(x) = eˣ is called the
natural exponential junction. For the
exponential function f(x) = eˣ, e is the constant
2.71828183…, whereas x is the variable.
Example 11
Use a calculator to calculate the expression.
a. e⁰∙⁰¹
b. e.⁰∙⁵
c. e. ⁰∙¹
d. e²
Solution to Example 11
Example 12
5. f(x) = 3ˣ⁻¹; x = 2, x = -2
Exercise B
Make a table of coordinates then graph each
function.
1. f(x) = 5ˣ 6. g(x) = 4⁻ˣ⁺²
x
2. f(x) = 6⁻ˣ 7. h(x) = 2
3
3. g(x) = -5ˣ x
4. f(x) = 3ˣ⁻² 8. f(x) = 1
x 1
3
5. f(x) =
1
2
Exercise C
Find the base of the exponential function whose
graph contains the given points.
1
1. (2, 16) 5. (4, )
625
2. (1, 10)
3
3. (3, 64) 6. ( , 27)
1 2
4. (3, )
343