Transcript 4.3 Writing and Graphing Functions

4.3 Writing & Graphing Functions
Algebra 16,17, 18
Writing Equations
Practice
• When an equation has two variables, its
solutions will be all ordered pairs (x,y) that
make the equation true.
• We can graph those solutions.
• When we graph all solutions of an equation,
that means we are graphing the equation.
• Recall that an equation with two variables is a
relation, and it may or may not be a function.
• One way to determine if a relation is a
function is to graph the equation, and then
use the vertical-line test.
Vertical Line Test - Functions
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Vertical Line Test - Functions
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Vertical Line Test - Functions
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Vertical Line Test - Functions
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Vertical Line Test - Functions
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Graphing Functions
Practice
Domain & Range of Functions
• Looking at the graph can help you find domain
and range.
Function Variables
• In a function you have independent and
dependent variables.
• Independent variable
– Usually x
– Does not depend on the other
• Dependent variable
– Usually y
– Depends on x
Function Notation
• If x is independent and y is dependent, the
function notation for y is f(x).
• You read f(x) as “f of x”.
• The f is the name of the function and x is the
independent variable.
Writing Functions
• Identify the independent and dependent
variables. Write a rule using function notation.
Evaluating Functions
Function Notation
y  2x  3
f (x)  2x  3
when x  1, y  5
f (1)  5
when x  2, y  7
f (2)  7
when x  3, y  9
f (3)  9
when x  4, y  11
f (4)  11
f ( 4)  5
Evaluate the function over the domain,
x = -1, x = 0, x = 2.
1) f (x)  4x
{4, 0, 8 }
2) g(x)  3x  9
{12,  9,  3 }
3) h(x)  x  1
2
{ 0,  1, 3 }
Review
• How do we write an equation from a table of
data?
• What is another test we can use to see if a
relation is a function or not?
• How do we graph functions?
• What are independent and dependent
variables?
• How do we evaluate functions?