12.2 functions and graphs f(x) = x+4 where the domain is {-2,-1,0,1,2,3}
TRANSCRIPT
12.2 Functions and Graphs
F(X) = x+4 where the domain is {-2,-1,0,1,2,3}
To determine if an equation is a function…
Create a (x, y) table
Is y = x² a function?
Is x = y2 a function?
No, because x = 9 is equal to both 3 and –3.
Is y = |x| a function?
Is x = |y| a function?
No, because x = 7 is equal to both 7 and –7.
YES
To determine if a graph is a function…
Perform the Vertical Line Test
Is this a graph of a function?
Vertical
Line
Test
Is this a graph of a function?
Is this a graph of a function?
Is this a graph of a function?
Is this a graph of a function?
Is this a graph of a function?
Domain of a Function
• X values have to make the value a real number
• Watch for 0 in the denominator
• Watch for – under the square root (set radicand )0
Find the domain of
Domain is {x | x 4}
1( )
4g x
x
Find the domain of
Domain is {x | x -5}
( ) 5h x x 5 0x
5x
Find the domain of
Domain is all real numbers
2( ) 7f x x
Find the domain of
Domain is {x | x 4}
3( )
4f x
x
Find the domain of
Domain is {x | x 7}
( ) 7g x x
7 0x 7x
Graph and State Domain and Range
• Domain is horizontal coverage
• Range is vertical coverage
Find the domain of f(x) = 2x + 1
Domain is all real numbers
Find the range of f(x) = 2x + 1
Range is all real numbers
Find the range of
( ) 2g x x x y024-2-4-6
Range is { y | y 0 }
x y0 22 44 6-2 0-4 2-6 4
x y024-2-4-6
Find the range of
( ) 1f x x x y0 -12 14 3-2 1-4 3-6 5
Range is { y | y -1 }
AssignmentPage 545
(2-10 even and 11-31all)