MATH 1310 Section 5.2.

Slides:

Advertisements

Similar presentations

Section 2.5 Transformations of Functions. Overview In this section we study how certain transformations of a function affect its graph. We will specifically.

Advertisements

Exponential Functions and Their Graphs Digital Lesson.

Graphs of Exponential and Logarithmic Functions

Section 1.6 Transformation of Functions

Create a table and Graph:. Reflect: Continued x-intercept: y-intercept: Asymptotes: xy -31/3 -21/2 1 -1/22 xy 1/ /2 3-1/3.

Exponential Functions and Their Graphs Section 3-1.

Section 3.2 Notes Writing the equation of a function given the transformations to a parent function.

6.5 - Graphing Square Root and Cube Root

What is the symmetry? f(x)= x 3 –x.

1 Factoring Practice (5 questions). 2 Factoring Practice (Answers)

(7.1 & 7.2) NOTES- Exponential Growth and Decay. Definition: Consider the exponential function: if 0 < a < 1: exponential decay if a > 1: exponential.

Exponential Functions and Their Graphs 2 The exponential function f with base a is defined by f(x) = a x where a > 0, a  1, and x is any real number.

Exponential Functions Evaluate Exponential Functions Graph Exponential Functions Define the number e Solve Exponential Equations.

Graphs & Models (Precalculus Review 1) September 8th, 2015.

Exponential & Logarithmic functions. Exponential Functions y= a x ; 1 ≠ a > 0,that’s a is a positive fraction or a number greater than 1 Case(1): a >

Graphing Exponential function parent function: y = 2 x X is the exponent!!! What does this look like on a graph? In the parent function the horizontal.

Math 71B 9.3 – Logarithmic Functions 1. One-to-one functions have inverses. Let’s define the inverse of the exponential function. 2.

(a) (b) (c) (d) Warm Up: Show YOUR work!. Warm Up.

Section 1.4 Transformations and Operations on Functions.

Exponential & Logarithmic functions. Exponential Functions y= a x ; 1 ≠ a > 0,that’s a is a positive fraction or a number greater than 1 Case(1): a >

Math – Exponential Functions

The base e P 667. Essential Question How is the graph of g(x) = ae x – h + k related to the graph of f(x) = e x.

Logarithmic Functions. How Tall Are You? Objective I can identify logarithmic functions from an equation or graph. I can graph logarithmic functions.

MATH 1310 Session 4.

Logarithmic Functions

Exponential Functions and Their Graphs Section 3-1

2.6 Families of Functions Learning goals

Section 6.2 – Graphs of Exponential Functions

Aim: What is the exponential function?

2.6 Translations and Families of Functions

How does one Graph an Exponential Equation?

Exponential Functions

1.2A Stretches The graph of y + 3 = f(x) is the graph of f(x) translated…  up 3 units  left 3 units  down 3 units  right 3 units x 2. The.

Exponential Functions and Their Graphs

MATH 1310 Session 8.

Exponential Functions, Growth and Decay Understand how to write and evaluate exponential expressions to model growth and decay situations. Do Now: - What.

Exponential Functions and Their Graphs

MATH 1310 Section 5.1.

Exponential Functions and Their Graphs

Characteristics of Exponential Functions

6.3 Logarithmic Functions

Graphing Exponential Functions Exponential Growth p 635

Chapter 3 Section 1 Exponential Functions and Their Graphs

Graphing Exponential Functions

4.2 Exponential Functions and Their Graphs

3.1 EXPONENTIAL & LOG FUNCTIONS

Unit 3: Exponential and Logarithmic Functions

2.7 Graphing Absolute Value Functions

3.1 Exponential Functions and Their Graphs

6.9 Graphing Exponential Equations

Exponential Functions and Their Graphs

Exponential Functions and Their Graphs Section 3-1

MATH 1310 Section 3.6.

Exponential Functions and Their Graphs

2.7 Graphing Absolute Value Functions

§ 8.3 Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions.

4.3 Logarithmic Functions

6.4a Transformations of Exponential Functions

Exponential Functions and Their Graphs

MATH 1310 Section 5.1.

4.3 Logarithmic Functions

MATH 1310 Section 3.6.

7.4 Graphing Exponential Equations

Exponential Functions and Their Graphs

MATH 1310 Section 5.1.

15 – Transformations of Functions Calculator Required

Exponential Functions and Their Graphs

MATH 1310 Section 5.2.

6.3 Exponential Functions

Warm up honors algebra 2 3/1/19

Presentation transcript:

MATH 1310 Section 5.2

The number “e.”

In case you were wondering, the letter “e” is used for this particular irrational number because of the mathematician Euclid used this constant extensively in his work. For instance: cos(x) + i sin(x) = eix Meaning that: eiπ = -1

Example 3: Write the equation of a natural exponential function that has been shifted left 3 units, down 1 unit and reflected in the x-axis.

Popper 28: Consider the function: f(x) = -ex-2 + 3. Determine the domain of the function: a. (-∞, ∞) b. (3, ∞) c. [3, ∞) d. (-2, ∞) 2. Determine the range of the function: a. (-∞, ∞) b. (-3, ∞) c. (-∞, 3) d. (-∞, 2) 3. Determine the y-intercept of the function: a. 1 b. e-2 + 3 c. 3 – e2 d. 3𝑒 2 −1 𝑒 2 4. Determine the asymptote of the function: a. y = e b. x = e c. y = 3 d. x = 3 5. Which transformation did not take place from g(x) = ex? Horizontal Shift b. Vertical Shift c. Horizontal Reflection d. Vertical Reflection

f(x) = -ex-2 + 3