Lesson (1.3) Graphs of Functions
How do we know when a graph represents a function?
Vertical Line Test--if all vertical lines intersect only one
point of the graph, then the graph represents a function.
Need to be able to use a graph of an equation to:
a) determine if the graph represents function or not and
explain why or why not
b) determine the domain and range of the function
Also need to be able to determine the domain and range
algebraically.
Increasing, Decreasing, and Constant Functions
Determine the open intervals on which each function is increasing, decreasing, or constant.
Determine the open intervals on which each function is increasing, decreasing, or constant.
Determine the open intervals on which each function is increasing, decreasing, or constant.
• Decreasing:
•
• Increasing:
•
• Constant:
when x1 < x2 then f(x1) > f(x2)
negative slope
when x1 < x2 then f(x1) < f(x2)
positive slope
when x1 < x2 then f(x1) = f(x2)
horizontal
Relative Minimum and Maximum Values
• A relative minimum exists when a graph changes from decreasing to increasing
­­considered a low point (note: not necessarily the lowest)
­­if there is more than one, they are called relative minima
• A relative maximum exists when a graph changes from increasing to decreasing
­­considered a high point (note: not necessarily the highest)
­­if there is more than one, they are called relative maxima
Use a calculator to approximate (to 2 decimal places) any relative minima or maxima.
standard window
max (0,1)
min (1.33, ­1.37)
Use a calculator to approximate (to 2 decimal places) any relative minima or maxima.