Functions PreCalculus 1-2.

Slides:



Advertisements
Similar presentations
Composition of functions constructing a function from 2 functions (g o f) = g[f(x)] –for all x in domain of f such that f(x) is in domain of g –f is applied.
Advertisements

Rational Functions Characteristics. What do you know about the polynomial f(x) = x + 1?
2.5 Piecewise- defined Functions
4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.
9.4 Properties of Logarithms. Since a logarithmic function is the inverse of an exponential function, the properties can be derived from the properties.
Name:__________ warm-up 9-5 R Use a table of values to graph y = x 2 + 2x – 1. State the domain and range. What are the coordinates of the vertex of the.
Lesson 5-5 Logarithms. Logarithmic functions The inverse of the exponential function.
A. What is the definition of Domain? B. What is the definition of Range? Your answers should be a complete sentence.
6.5 Applications of Common Logarithms
Derivatives of Inverse Trigonometric Functions
Chapter 1.3 Exponential Functions. Exponential function F(x) = a x The domain of f(x) = a x is (-∞, ∞) The range of f(x) = a x is (0, ∞)
Functions Relation such that each element x in a set A maps to EXACTLY ONE element y in a set B  Set A: Domain = set of all numbers for which the formula.
Chapter 1.5 Functions and Logarithms. One-to-One Function A function f(x) is one-to-one on a domain D (x-axis) if f(a) ≠ f(b) whenever a≠b Use the Horizontal.
5.5 – The Quadratic formula Objectives: Use the quadratic formula to find real roots of quadratic equations. Use the roots of a quadratic equation to locate.
Function Inverse Quick review. {(2, 3), (5, 0), (-2, 4), (3, 3)} Domain & Range = ? Inverse = ? D = {2, 5, -2, 3} R = {3, 0, 4}
Change & Evaluate the following Logarithmic Equations to Exponential Equations.
3.4 Properties of Logarithmic Functions
Domain/Range/ Function Worksheet Warm Up Functions.
2.1 GRAPHING LINEAR EQUATIONS GOAL: FIND DOMAIN AND RANGE. DETERMINE IF RELATIONS ARE FUNCTIONS. GRAPH LINEAR EQUATIONS.
f(x)= 2x – 15 f(-4)= 2(-4) – 15 f(-4)= (-8) – 15 f(-4)= -23.
Function Composition Given f(x) = 2x + 2 and g(x) = 2, find f ºg(x). f ºg(x)=f(g(x)Start on the inside. f(g(x)) g(x) = 2, so replace it. f(g(x)) = f(2)
Objective: Students will be able to write equivalent forms for exponential and logarithmic functions, and can write, evaluate, and graph logarithmic functions.
Tell Me Everything You Can About The Graph Below.
LEQ: How do you evaluate logarithms with a base b? Logarithms to Bases Other Than 10 Sec. 9-7.
Warm Up  1.) Write 15x 2 + 6x = 14x in standard form. (ax 2 + bx + c = 0)  2.) Evaluate b 2 – 4ac when a = 3, b = -6, and c = 5.
Warm Up Simplify. x 3w z x – 1 1. log10x 2. logbb3w 3. 10log z
6.5 Applications of Common Logarithms Objectives: Define and use the common logarithmic function to solve exponential and logarithmic equations. Evaluate.
Functions and Their Graphs
3.2 Functions.
Piecewise Functions At least 2 equations, each of which applies to a different part of the functions domain. It is like having 3 equations for 3 different.
College Algebra Chapter 2 Functions and Graphs
Prerequisite Skills VOCABULARY CHECK 1
UNIT SELF-TEST QUESTIONS
Complex Numbers and Roots
1-1 RELATIONS & FUNCTIONS
Unit 1B quadratics Day 6.
Logarithmic Functions and Their Graphs
Exponential Functions
FUNCTIONS Chapter 1 Section 4.
A function is given by a formula. Determine whether it is one-to-one
Objective 1A f(x) = 2x + 3 What is the Range of the function
Today in Precalculus Go over homework Notes: Remainder
Piecewise Functions At least 2 equations, each of which applies to a different part of the functions domain. It is like having 3 equations for 3 different.
Relations and Function
Properties of Logarithmic Functions
Graphing and Evaluating The Piecewise Function A Series of Examples
Warm Up Given y = –x² – x + 2 and the x-value, find the y-value in each… 1. x = –3, y = ____ 2. x = 0, y = ____ 3. x = 1, y = ____ –4 – −3 2 –
Chapter 3 Section 6.
College Algebra Chapter 2 Functions and Graphs
Exponential Functions
Lines in the Plane PreCalculus 1-1.
DO NOW Homework: Lesson 5-2 Practice (pg. 75)
Composition OF Functions.
Composition OF Functions.
Graphs of Functions FUNCTIONS AND THEIR GRAPHS Essential Questions:
Functions and graphs Sec 7 1-C pg
1.5 Combination of Functions
By the end of this lesson, you will know how to: Evaluate a function
Unit 3 Functions.
Function Composition.
Characteristics.
4.3 Use Functions Involving e
Section 1 – Relations and Functions
Warm-up 5/22/2019 Day 6.
2.7 Piecewise Functions Algebra 2.
Exponential Functions
2.1 Functions.
Characteristics.
5.3 Solving Trigonometric Equations
FUNCTIONS & THEIR GRAPHS
Presentation transcript:

Functions PreCalculus 1-2

Functions

Functions

Functions

Functions

Functions

Let f(x) = 5x2 + x – 6 Evaluate f(-5) f(-5) = 114 Functions

Functions

Functions

Functions

Functions

Why are functions better than other equations? Think Deep

Quick Questions Define Domain Define Range Can the domain be all real numbers, but the range is not? Is this still a function? Example? Another example? Can the range be all real numbers, but the domain is not? Quick Questions

Functions

Functions

Find the domain of the function Functions

Functions

Functions

Find formulas for the following functions Exploration

Find formulas for the following functions Exploration

Homework pg. 24 – 29 7, 9, 28, 33, 36, 51, 53, 72 Functions