1. CHAPTER 2
SECTION 1

2. Basics of Functions and Their Graphs
Goal: find domain and range, determine if a relation
is a function, determine if an equation is a function,
evaluate a function, graph a function, use the vertical
line test, interpret graphs, and find intercepts.
A relation is any set of ordered pairs.
{(2,7),(-3,5),(4,-2),(1,9),(-4,5)}
The domain is the set of x-values.
The range is the set of y-values.

3. A function is a correspondence from the first set, called the domain,
to a second set, called the range, such that each element in the
domain corresponds to exactly one element in the range.
Determine if each relation is a function:
Determining if a relation is a function:
Do any of the x-values repeat?
no, then the relation is a fucntion
yes, go to step two
If an x repeats, does it have the same y value?
yes, then the relation is a function.
no, then the realation is not a function.
{(2,5),(-1,9),(8,12),(-5,0)}
{(2,9),(-3,7),(2,9),(12,5)}
{(12,0),(3,4),(0,7),(3,-4)}

4. Determining Whether an Equation Represents a Function.
1. x2 + y = 4
Solve each equation for y and
determine if the equation has
multiple values for x at a given y.
2. x2 + y2 = 16

5. Evaluating a Function
f(x) = x2 + 3x + 5
f(2)
f(x + 3)
f(-5)
f(-x)

6. Graphing Functions
f(x) = 2x
f(x) = x2 – 5
f(x) = │x│ + 3

7. Vertical Line Test
If any vertical line intersects a graph in more than one point,
then the graph does not define y as a function of x. 1. 2.

8. 3.

9. Analyzing the graph of a function, Domain and Range:
Is f(x) a function? Explain.
Estimate f(5)
For what value is f(x) = 3
What is the domain?
What is the range?

10. HOMEWORK
PAGE
{2-6,12-18,28-32,40-46,52-64}
EVENS
{65-80}
ALL