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 PROBLEMEXPONENTIAL RULES ANSWER 2x ⁵ * (-7x⁶) Same base-add exponents; multiply coefficients -14x ¹¹ 2x ⁵ * (-7y⁶) Different base-multiply coefficients -14x ⁵y⁶ Same base-subtract exponents; divide coefficients 3x ¹² Same base-subtract exponents; divide coefficients (5x ⁶)ᶟ Multiply exponents; Raise coefficients to the power 125x ¹⁸ Different base-Multiply exponents; Divide coefficients. Raise coefficient to the power ((2x³)²) ⁵ Multiply exponents. Raise coefficient to the power 1024x³º Inverse of base. Negative of exponent x³

Exponential Function: 8.2 Remember??? Basic Linear Function: y= x Basic Quadratic Function: y=x² 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

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 y- axis To solve replace x-values with 0 Domain- x-values of a function (- ∞, ∞) Range- y-values of a function (0, y- intercept 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 Function Highlights: Exponential Functions rise or falls rapidly from left to right Exponential functions never touch the x- axis If you have a POSITIVE exponent the graph rises from left to right above the x-axis; graph is located in Quadrant 1 If you have a NEGATIVE exponent the graph falls from left to right above the x- axis; the graph is in Quadrant 2

Exponential Function: 8.2 Exponential Function Highlights: If you have a NEGATIVE coefficient and a POSITIVE exponent the graph will fall from left to right below the x-axis; the graph is located in Quadrant 4 If you have a NEGATIVE coefficient and a NEGATIVE exponent the graph will rise from left to right below the x-axis; the graph is located in Quadrant 3

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 Quadrant 1 Graph: y= 2 ˣ, 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=.9 ˣ, y=.1ˣ, y=.45ˣ, y=.25ˣ

Exponential Function: 8.2 TOTD: 1) What is the difference between an exponential function and a linear/quadratic function?

Exponential Function: 8.2 Homework Redo Exponential Properties Review pg (6-16)

Exponential Function: 8.2 Activation: pg. 343 Warm Up & Motivator Instruction: Notes on Domain, Range, Zeroes, Intercepts Work: Complete Guided Practice Examples- Problem 1 & 2 Assessment: Unit 5 Quiz 1 Summary: What is the difference between an exponential function and a linear/quadratic function?