Domain and range.

Slides:



Advertisements
Similar presentations
Exponential Functions and Their Graphs Digital Lesson.
Advertisements

EXAMPLE 4 Graph a translated square root function Graph y = –2 x – Then state the domain and range. SOLUTION STEP 1 Sketch the graph of y = –2 x.
Functions Domain and range The domain of a function f(x) is the set of all possible x values. (the input values) The range of a function f(x) is the set.
DO NOW: 6.3: w/s C: Perform the indicated operation. 1.) Find g(f(x)) if f(x) = 2x 2 – x and g(x) = 2.) Find g(h(8)) if g(x) = -x 2 and h(x) =
What is the symmetry? f(x)= x 3 –x.
Product and Quotients of Functions Sum Difference Product Quotient are functions that exist and are defined over a domain. Why are there restrictions on.
Math – What is a Function? 1. 2 input output function.
1 Solve each: 1. 5x – 7 > 8x |x – 5| < 2 3. x 2 – 9 > 0 :
2.1 “Relations & Functions” Relation: a set of ordered pairs. Function: a relation where the domain (“x” value) does NOT repeat. Domain: “x” values Range:
Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x f(x) = x + 4, g(x) = x
Inverse functions: if f is one-to-one function with domain X and range Y and g is function with domain Y and range X then g is the inverse function of.
1.1 - Functions. Ex. 1 Describe the sets of numbers using set- builder notation. a. {8,9,10,11,…}
INVERSE Logarithmic and Exponential Graphs and Graphing.
5.3- Inverse Functions If for all values of x in the domains of f and g, then f and g are inverse 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.
Functions Learning Objectives To understand function notation
Functions JEOPARDY.
Basic Math Skills.
Functions.
7.4 Functions Designed by Skip Tyler.
Notes Over 2.1 Function {- 3, - 1, 1, 2 } { 0, 2, 5 }
Functions Review.
Domain and range.
Objective 1A f(x) = 2x + 3 What is the Range of the function
Exponential Functions and Their Graphs
Rational Functions, Transformations
Exponential Functions and Their Graphs
Before: October 19, 2017 A function is represented by f (x) = 2x + 5. Find f (3). Create a table representing the above function with a domain: {1,2,3,4}
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.
Chapter 3 Section 1 Exponential Functions and Their Graphs
4.2 Exponential Functions and Their Graphs
Relations and Function
Objectives The student will be able to:
Graphing and Evaluating The Piecewise Function A Series of Examples
Partner Whiteboard Review.
Function notation.
Activity 2.8 Study Time.
Modulus Function.
Quadratics graphs.
Functions.
3.1 Exponential Functions and Their Graphs
2-6: Combinations of Functions
Composition OF Functions.
2.6 Operations on Functions
Composition OF Functions.
Exponential Functions and Their Graphs
1.2 Analyzing Graphs of Functions and Relations
Functions Inverses.
Functions Inverses.
3.5 Operations on Functions
Warm Up Determine the domain of the function.
Objectives The student will be able to:
By the end of this lesson, you will know how to: Evaluate a function
Modulus Function.
Functions and Relations
Functions.
Unit 3 Functions.
Warm Up Determine the domain of f(g(x)). f(x) = g(x) =
Function And Relations Review
Exponential Functions and Their Graphs
Exponential Functions
Review: How do you find the inverse of a function? Application of what you know… What is the inverse of f(x) = 3x? y = 3x x = 3y y = log3x f-1(x) = log3x.
2.1 Functions.
Objectives The student will be able to:
Objectives The student will be able to:
Exponential Functions and Their Graphs
2-6: Combinations of Functions
f(x) g(x) x x (-8,5) (8,4) (8,3) (3,0) (-4,-1) (-7,-1) (3,-2) (0,-3)
Review for Test #1 Calculus – Larson.
Functions BY : Ms. MANITA.
Presentation transcript:

Domain and range

Sketch a graph to help figure it out Domain: The domain is the set of all possible x-values which will make the function "work", and will output real y-values. Range: The range is the resulting y-values we get after substituting all the possible x-values Sketch a graph to help figure it out Range Domain

Ten questions Range

What is the range of f(x) What is the range of g(x) 𝑓 𝑥 = 4𝑥−2 8−𝑥 𝑥<2 𝑥≥2 𝑔 𝑥 = 1−3𝑥 𝑥−11 𝑥<3 𝑥≥3 range of f(x) ≤𝟔 range of f(x) ≥−𝟖

𝑓 𝑥 =3 𝑥 2 −2 𝑔 𝑥 =3− 𝑥 2 What is the range of f(x) What is the range of g(x) 𝑓 𝑥 =3 𝑥 2 −2 𝑔 𝑥 =3− 𝑥 2 range of y= x2 is y≥0 range of y= =3x2 is y≥0 range of f(x) ≥ −𝟐 range of f(x) ≤ 𝟑

What is the range of f(x) What is the range of g(x) 𝑓 𝑥 = 7 8− 𝑥 2 𝑥<−1 −1≤𝑥<∞ 𝑔 𝑥 = 𝑥−6 𝑥 2 −6 𝑥<0 𝑥≥0 range 𝑓 𝑥 ≤8 range 𝑓 𝑥 𝜖 𝑹

𝑔 𝑥 = 7 𝑥 2 −3, 𝑓 𝑥 = 8−𝑥 , What is the range of f(x) What is the range of g(x) 𝑔 𝑥 = 7 𝑥 2 −3, 𝑓 𝑥 = 8−𝑥 , range 𝑓 𝑥 ≥0 range 𝑔 𝑥 ≥−3

𝑓 𝑥 = 1 𝑥−2 , 𝑥≠2 𝑔 𝑥 = (4−𝑥) 3 , −2<𝑥<6 9 of 10 10 of 10 What is the range of f(x) What is the range of g(x) 𝑓 𝑥 = 1 𝑥−2 , 𝑥≠2 𝑔 𝑥 = (4−𝑥) 3 , −2<𝑥<6 range 𝑓 𝑥 ≠0 𝑓 𝑥 ∈𝑅 range −8≤𝑔 𝑥 ≤216

One thing to improve is – KUS objectives BAT understand domain and range of functions BAT define functions from graphs self-assess One thing learned is – One thing to improve is –

END