Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely.

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Presentation transcript:

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph.

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. LINEAR

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. LINEAR Graphing techniques : 1.Slope – intercept 2.Create an x / y table

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. LINEAR Graphing techniques : 1.Slope – intercept 2.Create an x / y table EXAMPLE : Graph

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. LINEAR Graphing techniques : 1.Slope – intercept 2.Create an x / y table EXAMPLE : Graph m = 2 b = ( 0, - 4 )

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. LINEAR Graphing techniques : 1.Slope – intercept 2.Create an x / y table EXAMPLE : Graph - 4 m = 2 b = ( 0, - 4 ) Starting at ( 0, - 4 ), count a slope of 2 ( up 2 then right 1) and plot a new point ( 1, -2 ) and sketch your line

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. QUADRATIC

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. QUADRATIC Graphing techniques : 1.Find the vertex 2.Find any x – intercepts 3.Find the y – intercept 4.Use the axis of symmetry to plot a symmetry point in relation to the y – intercept 5.Plot some points

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. QUADRATICEXAMPLE : Graph

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. QUADRATICEXAMPLE : Graph Y – intercept ( where x = 0 )

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. QUADRATICEXAMPLE : Graph Y – intercept ( where x = 0 ) Plot some points :

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. ABSOLUTE VALUE

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. ABSOLUTE VALUE Graphing techniques : 1.Find the vertex or “bounce” 2.Plot one point on either side of the vertex

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. ABSOLUTE VALUE EXAMPLE : Graph

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. ABSOLUTE VALUE EXAMPLE : Graph

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. ABSOLUTE VALUE EXAMPLE : Graph

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. CUBIC

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. CUBIC Graphing techniques : 1.Find the y - intercept 2.Plot a few points on either side of the y – intercept ** these are used only on the basic cubic functions that do not contain a quadratic or linear part. We will cover those in a later section.

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. CUBIC Graph :

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. CUBIC Graph : Find the y – intercept

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. CUBIC Graph : Find the y – intercept Plot a few points on either side :

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. SQUARE ROOT

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. SQUARE ROOT Graphing techniques : 1.Find the domain 2.Plot some points starting with the restricted end of the domain.

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. SQUARE ROOTEXAMPLE : Graph

Graphs of Functions It essential in any higher mathematics to understand the basic shapes of all functions. This section will look at the five most widely used functions and how to quickly sketch their graph. SQUARE ROOTEXAMPLE : Graph Domain : [ -2, + ∞ )