Graphs of Functions The graph of a function gives you a visual representation of its rule. A set of points generated like we did in the previous section. You can determine if a given graph is a true function by the VERTICAL LINE TEST. Given the graph of a relation, the vertical line test is used to check if that relation is a function. The vertical line CAN NOT touch the graph in more than 1 spot.

Graphs of Functions VERTICAL LINE TEST – a vertical line drawn anywhere on the graph CAN NOT intersect the graph more than once. Here is the graph of a relation. Is it a true function ?

Graphs of Functions VERTICAL LINE TEST – a vertical line drawn anywhere on the graph CAN NOT intersect the graph more than once. Here is the graph of a relation. Is it a true function ? YES…I can not draw a vertical line that passes thru the graph more than once

Graphs of Functions VERTICAL LINE TEST – a vertical line drawn anywhere on the graph CAN NOT intersect the graph more than once. Here is the graph of a relation. Is it a true function ?

Graphs of Functions VERTICAL LINE TEST – a vertical line drawn anywhere on the graph CAN NOT intersect the graph more than once. Here is the graph of a relation. Is it a true function ? NO…I only need to find one spot where a vertical line crosses more than one time.

Graphs of Functions One-to-One Functions – a function where each range value has one and ONLY one domain value. Horizontal line test checks for one-to-one… Here is the graph of a function. Is it one-to-one ?

Graphs of Functions One-to-One Functions – a function where each range value has one and ONLY one domain value. Horizontal line test checks for one-to-one… Here is the graph of a function. Is it one-to-one ? NO…I only need to find one spot where a horizontal line crosses more than one time.

Graphs of Functions One-to-One Functions – a function where each range value has one and ONLY one domain value. Horizontal line test checks for one-to-one… Here is the graph of a function. Is it one-to-one ?

Graphs of Functions One-to-One Functions – a function where each range value has one and ONLY one domain value. Horizontal line test checks for one-to-one… Here is the graph of a function. Is it one-to-one ? YES…I can not draw a vertical line that crosses more than one time.

Graphs of Functions One-to-One Functions – a function where each range value has one and ONLY one domain value. Horizontal line test checks for one-to-one… Functions that are not one-to-one have NO INVERSE !!!

Graphs of Functions Graphing functions falls into two categories… 1. Continuous or constant functions ( no breaks ) 2. Piecewise functions…breaks in the graph occur We will first look at the Continuous Functions… Steps :1. Create a table of values for f(x) 2. Plot the points and sketch your graph

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x 2 – 5

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x 2 – 5 xf(x) - 2 f(-2) = (-2) 2 -5 f(-2) = 4 – 5 f(-2) = -1

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x 2 – 5 xf(x) f(-1) = (-1) 2 -5 f(-1) = 1 – 5 f(-1) = - 4

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x 2 – 5 xf(x) f(0) = (0) 2 -5 f(0) = 0 – 5 f(0) = - 5

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x 2 – 5 xf(x) f(1) = (1) 2 -5 f(1) = 1 – 5 f(1) = - 4

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x 2 – 5 xf(x) f(2) = (2) 2 -5 f(2) = 4 – 5 f(2) = -1

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x 2 – 5 xf(x) Plot the points…

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x 2 – 5 xf(x) Sketch your graph…

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x xf (x) f(-3) = (-3) f(-3) = f(-3) = -25

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x xf (x) f(-2) = (-2) f(-2) = f(-2) = -6

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x xf (x) f(-1) = (-1) f(-1) = f(-1) = 1

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x xf (x) f(0) = (0) f(0) = 0+ 2 f(0) = 2

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x xf (x) f(1) = (1) f(1) = f(1) = 3

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x xf (x) f(2) = (2) f(2) = f(2) = 10

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x xf (x) f(3) = (3) f(3) = f(3) = 29

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x xf (x) Plot your points…

Graphs of Functions Steps :1. Create a table of values for ƒ(x) 2. Plot the points and sketch your graph EXAMPLE :Graph ƒ(x) = x xf (x) Sketch the graph…