### Exponential Function: 8.4

```Exponential Functions: 8.2
Properties of Exponential Functions Part 1: Domain
and Range, Zeros, and Intercepts
Exponential Functions: 8.2
Activation: Warm Up pg. 343 B & Motivator
Region Tournament-Tutoring/E2020
Quiz #1 B-DAY 2/23
A-DAY 2/24
Exponential Functions: 8.2
IMPORTANT DATES
QUIZ #1 B-DAY 2/23
A-DAY 2/24
MidUnit Test A-DAY 3/5
B-DAY 3/6
Quiz # 2 A-DAY 3/15
B-DAY 3/16
Unit Test B-DAY 3/22
A-DAY 3/23
Exponential Functions: 8.2
EQ: What is the basic exponential function?
Today we will review how to graph an
Exponential Functions!!
Exponential Functions: 8.2

b. Investigate and explain characteristics
of exponential functions, including domain
and range, asymptotes, zeros, intercepts,
intervals of increase and decrease, rates
of change, and end behavior.
Exponential Functions: 8.2
Review Homework Examples:
Pg. 495 (6-9)
Pg.496 (13-16)& (25-28)
Page p.495/496
#8, 11, 15, 19, 25, 27
Exponential Worksheet
#13, 15, & 17
Exponential Functions: 8.2
**Remember when you have a negative
exponent, you will flip over the fraction far
(place the exponent in the opposite
segment of the division bar:
numerator/denominator) and make the
exponent POSITIVE.**
**You only flip the variable attached to the
exponent; not the coefficient**
Examples:
Exponential Functions: 8.2
PROBLEM
EXPONENTIAL
RULES
2x⁵ * (-7x⁶)
exponents; multiply
coefficients
-14x¹¹
2x⁵ * (-7y⁶)
Different base-multiply
coefficients
-14x⁵y⁶
Same base-subtract
exponents; divide
coefficients
3x¹²
Same base-subtract
exponents; divide
coefficients
(5x⁶)ᶟ
Multiply exponents;
Raise coefficients to the
power
Different base-Multiply
125x¹⁸
Exponential Function: 8.2
Remember???
Basic Linear Function: y= x
Fact: Unlike Linear and Quadratic Functions,
the basic Exponential Function is not a single
function
Fact: Exponential Functions depends on the
BASE of the Exponential Function
Exponential Function: 8.2
The Basic Exponential Function is written as
y=   for b>0 , b≠ 1 , and x is ANY real number, and b is a positive number
Variable x is now the power (exponent), rather than the base like with a
linear function
Problem #2 page 346 # 1, 3, 4, 5, & 6
Complete Table and Graph
Key Terms Review:
Zeros (Solutions, X-intercepts)- Set of x-values such that f(x)=0
Ex: x + 3= 0
X =-3
X-intercepts- are the x-coordinate (x-value) of the point where a graph
crosses the x-axis.
◦ The values at which the graph crosses the x-axis
◦ To solve set y or f(x) equal to 0 and solve
Exponential Function: 8.2
Y-intercept
 The y-intercept is the y-coordinate of the
point where a graph crosses the y-axis.
 The values at which the graph crosses the yaxis
 To solve replace x-values with 0
Domain- x-values of a function (-∞, ∞)
Range- y-values of a function (0, yintercept value)
Exponential Function: 8.2
Exponential Growth (positive
exponent)/Decay (negative exponent or the
base is 0 or 1) Problems are examples of
Exponential Functions
Exponential Function: 8.2
Exponential functions with a base > 1
(whole #) have the following characteristic:

• the higher the number for the base the CLOSER
the graph will be to the y-axis/ steeper graph in
Graph: y= 2ˣ, y= 3ˣ, y=4ˣ, y=5ˣ
Exponential Function: 8.2

Exponential functions with a base
between 0 and 1 (fraction) has the
following characteristics:
 The smaller the fraction or decimal the closer the
graph is to the y-axis in Quadrant 2
 The graph falls from left to right (decreases)
Graph y= .9ˣ, y= .1ˣ, y= .45ˣ, y=.25ˣ
Exponential Function: 8.2
TOTD:
1) What is the difference between an
function?
Exponential Function: 8.2
Homework
Redo Exponential Properties Review
pg. 501-503(6-16)
Exponential Function: 8.2
Activation: pg. 343 Warm Up & Motivator
Instruction: Notes on Domain, Range,
Zeroes, Intercepts
Work: Complete Guided Practice ExamplesProblem 1 & 2
Assessment: Unit 5 Quiz 1
Summary: What is the difference between
an exponential function and a