Functions Chapter 4. What makes a graph a function? The graph passes the vertical line test PassesFails.

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Functions Chapter 4

What makes a graph a function? The graph passes the vertical line test PassesFails

What makes a graph a function? Each domain (x-value) is mapped to only one range (y- value). We create a “mapping” to see if a relation (set of ordered pairs) is a function.

Domain & Range Domain: all x-values List in braces from least to greatest and do not repeat values Range: all y-values List in braces from least to greatest and do not repeat values

Domain & Range Example {(3, 4), (-2, 7), (9, 10), (9, 11)} Domain {-2, 3, 9} Range {4, 7, 10, 11}

Mapping Diagram (4, 5), (-2, 7), (3, 7), (0, -1) -2 0 3 4 5 7 FUNCTION: 4 6 -3 0 2 NOT A FUNCTION: (4, 5), (4, -3), (-1, 2), (6,0) 5 Try using the vertical line test…does the relation pass?

Make a Table, Mapping, & Graph {(9, 2), (-3, 4), (1, 5), (-1, 2)} Table Mapping Graph

Types of Functions Linear Quadratic Absolute Value Exponential Cubic

Let’s GRAPH! Create a T-Chart x y

Graphing Continued: Pick values for x. Plug in x and use PEMDAS to solve for y. Plot ordered pairs. Connect the points. Include arrows at the end of your line. CHECK your work

Try these linear functions: 1. y = 3x + 1 2. y = -2x + 3 3. y = x – 4 What patterns do you see between the equations and the graph?

Functions Chapter 4

What makes a graph a function? The graph passes the vertical line test PassesFails

What makes a graph a function? Each ____________________ is mapped to only one ___________ ______________. We create a “________________” to see if a ________________ (set of ordered pairs) is a ________.

Domain & Range Domain: all x-values List in braces from least to greatest and do not repeat values Range: all y-values List in braces from least to greatest and do not repeat values

Domain & Range Example {(3, 4), (-2, 7), (9, 10), (9, 11)} Domain ____________________ Range _____________________

Mapping Diagram (4, 5), (-2, 7), (3, 7), (0, -1) FUNCTION: NOT A FUNCTION: (4, 5), (4, -3), (-1, 2), (6,0) Try using the vertical line test…does the relation pass?

Make a Table, Mapping, & Graph {(9, 2), (-3, 4), (1, 5), (-1, 2)} Table Mapping Graph

Types of Functions Linear Quadratic Absolute Value Exponential Cubic

Let’s GRAPH! Create a T-Chart

Graphing Continued: Pick values for _____. Plug in x and use _______ to solve for __. Plot ordered ______. Connect the _________. Include ________ at the end of your line. _________ your work

Try these linear functions: 1. y = 3x + 1 2. y = -2x + 3 3. y = x – 4 What patterns do you see between the equations and the graph?

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