1. Section 1.2 Introduction to Relations and Functions
2. Set-Builder Notation ex.
“the set of all x such that
x is greater than or equal to –3”
3. Interval Notation ex.
“the set of numbers greater than or equal to –3”
4. Relation Relation- is a set of ordered pairs
** The ordered pairs are denoted by (x, y) **
Domain- the set of all x-values
Range- the set of all y-values
5. Function (A special relation) Function- a relation in which each element in the domain corresponds to exactly one element in the range.
*For each x-value, there is exactly one y-value.*
Domain- the set of all x-values (independent variable)
Range- the set of all y-values (dependent variable)
6. Function We are going to be dealing with functions where we think of the . . .
function- as a rule that tells how to determine the dependent variable for a specific value of the independent variable.
7. Four Ways to Represent a Function Verbally (description in words)
Numerically (by a table of values)
Visually (by a graph)
Algebraically (by a formula)
8. A Function Verbally p. 16
ex. The amount of sales tax depends on the amount of the purchase.
9. A Function Numerically Use a table of values:
10. A Function Visually Any function can be visually represented
by a graph.
11. Vertical Line Test If every vertical line intersects a graph in no more than one point, then the graph is the graph of a function
12. A Function Algebraically f(x) = 3x + 10
To solve a function: Evaluate the
13. Function Notation “y is a function of x”
y depends on x
y = f (x)
f (x) is just another name for y !
ex. f(x) = 3x + 10