Vocabulary
Increasing- The graph rises from left to right for all real numbers.
Decreasing- The graph falls from left to right for all real numbers.
Odd Function- If f(-x) = -f(x) for all x in its domain. The graph is symmetric about the origin.
Even function- If f(-x) = f(x) for all x in its domain. The graph is symmetric about the y axis.
Decreasing- The graph falls from left to right for all real numbers.
Odd Function- If f(-x) = -f(x) for all x in its domain. The graph is symmetric about the origin.
Even function- If f(-x) = f(x) for all x in its domain. The graph is symmetric about the y axis.
Essential Information
Average Rate of Change
For a linear function, the rate of change is constant and is indicated by the slope. Even for a nonlinear function, however, the average rate of change over any interval can be found by finding the slope of the segment that connects the points on the graph determined by the endpoints of the interval. The graph of f(x) = log₃x shows that f(x) is always increasing. The slope between the labeled pairs of points decreases as x increases, that is, the average rate of change is decreasing over successive x intervals. So, although the graph is always rising, the rise becomes slower and slower for greater and greater x values. |
Even and Odd Functions
A function f is an even function if f(x) = f(x) for all x in its domain. The graph of an even function is symmetric about the y axis. A function f is an odd function if f(x) = -f(x) for all x in its domain. The graph of an odd function is symmetric about the origin.
A function f is an even function if f(x) = f(x) for all x in its domain. The graph of an even function is symmetric about the y axis. A function f is an odd function if f(x) = -f(x) for all x in its domain. The graph of an odd function is symmetric about the origin.