1. Analyzing Graphs of Functions
Sec. 2.3
Analyzing Graphs of Functions

2. Graph of a Function Ordered pairs (x, f(x)) where x is in the domain
If it is a function its x-intercept is at (a, 0)
“a” is a zero of the function

3. Zeros Value for which f(x) = 0 f(x) = x2 – 4 0 = x2 – 4 0 = (x+2)(x-2)
Look at ex. 3 p. 202

4. Domain And Range Determining Domain from the graph
The x values on the graph from left to right
If solid or a closed dot it means it includes that x value
If an open dot is used, that number is not included
P. 200 figure 2.26

5. Determining Range from the graph
The y values on the graph from bottom to top
Ex. 1 p. 200
If dots are not on the ends of the graph it continues on
P. 202 figure 2.28

6. Vertical Line Test
A graph is a graph of a function if and only if a vertical line does not intersect the graph at more than 1 point
P. 201 Ex. 2
P. 207 # 9

7. Increasing and Decreasing Functions
A function increases if for x1 & x2 in the interval x1 < x2 implies f(x1) < f(x2)
A function decreases if for x1 & x2 in the interval x1 < x2 implies f(x1) > f(x2)
A function is constant if for x1 & x2 in the interval x1 < x2 implies f(x1) = f(x2)

8. Ex. 4 p. 203
The points where a function changes from increasing, decreasing, or constant are often the maximum and minimum values of the function.
If you are just looking at a section of the graph (like fig p. 204), we can call them relative maximums and relative minimums

9. HW P. 207
9 - 12, 13, 16, 17 – 22, 23 – 31 odd, 39 – 53 odd