Relations and Functions
Evaluating with Function Notation
Linear vs Nonlinear Functions
Vocabulary
100
A relation that pairs each input with exactly one output is a _________________.
Function
100
f(x) = 3x - 5
f(2) = ?
f(2) = 1
100
Is the function linear or nonlinear?
Nonlinear
100
The set of all y values or outputs in a function is...
What is range?
200
Is the relation a function?
YES!
200
d(x)=1/2 x - 5
d(-2) = ?
d(-2) = -6
200
Is the function linear or nonlinear?
Nonlinear
200
The set of all x values or inputs in a function is...
What is domain?
300
Is relation a function?
NO :(
300
Find the range for the domain {-5, 1, 0, 3}
f(x) = 3x + 5
Range: {-10, 8, 5, 14}
300
Explain how to tell if a function in a table is linear or nonlinear.
As the input increases, the output must increase by the same increment each time.
300
A set of ordered pairs
What is relation?
400
List the ordered pairs in the mapping diagram. Is it a function?
(-4, 2) (-2,-1) (-2, 1) (0, 0)
No, it is not a function.
400
Find the value of x for the given value of f(x).
f(x)=5x-1 when f(x)=14?
3
400
a. nonlinear, as the x doesn't increase by the same number each time.
b. Tree B, it will be more than 23 ft tall, tree A will only be 20 ft tall.
400
A set of ordered pairs where no x values repeat, each x has a unique y.
What is a function?
500
Graph the points. Is it a function?
Not a function
500
Write a function rule for the statement "The output is 3 less than 5 times the input." Then complete the table.
y=5x-3
1 2 3 4
2 7 12 17
500
*Challenge*
The ordered pairs represent a function. Describe the pattern OR write an equation that describes the points. 
square the x value and subtract 1
y=x2-1
500
A function that often includes exponents or x in the denominator.
What is a nonlinear function?