Analyzing Graphs of Functions Sec. 2.3 Analyzing Graphs of Functions

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

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

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

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

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

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)

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. 2.33 p. 204), we can call them relative maximums and relative minimums

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