Increasing and Decreasing Functions Relative Maxima and Relative
- Slides: 20
§ § Increasing and Decreasing Functions Relative Maxima and Relative Minima Even and Odd Functions and Symmetry Functions and Difference Quotients
State the intervals on which the given function is increasing, decreasing, and constant. Constant: none Go from left to right like you’re walking a trail. Remember to use x-coordinates.
Constant: none Go from left to right like you’re walking a trail. Remember to use x-coordinates.
* (Also known as local maxima and local minima) Keep it simple. These are the points at which the function changes its increasing or decreasing behavior. They are the turning points.
Where are the relative maxima? Where are the relative minima? Where are the turning points?
* The function passes through the origin. The left and right sides of the graph are reflections of each other. Notice that the y-coordinate stays the same.
The alternate opposite sides show symmetry to each other. The function passes through the origin.
It is an even function. It passes through the origin. It is symmetrical on both sides of the y-axis.
The function is odd. It passes through the origin. The alternate opposite sides show symmetry to each other.
EVEN FUNCTIONS Algebraically: f(-x) = f(x) for all x in the domain of f. This means you take the function and plug in –x for x. If you end up with the original equation, it is an even function or symmetric with respect to the y-axis.
ODD FUNCTIONS Algebraically: f(-x) = -f(x) for all x in the domain of f. This means you take the function and plug in –x for x. If you end up with the opposite of the original equation – it is an odd function or symmetric with respect to the origin.
Verifying Algebraically….
Odd Even Neither
The Difference Quotient The difference quotient of a function f is an expression of the form where h ≠ 0. Where does it come from? The difference quotient, allows you to find the slope of any curve or line at any single point.
Steps Used in Finding A Difference Quotient
- Classify each decreasing function as having a slope
- Lesson 4 increasing and decreasing functions
- Lesson 5 increasing and decreasing functions
- Strictly increasing and decreasing functions
- Increasing decreasing and constant functions
- Increasing decreasing and piecewise functions
- Absolute max vs local max
- Difference between fresnel and fraunhofer diffraction
- Ordinary language examples
- How to find increasing and decreasing intervals on a graph
- Removable and non removable discontinuities
- Increasing and decreasing intervals
- Increasing and decreasing recipes
- Features of a parabola
- Graphing transformations
- Increasing at a decreasing rate
- Relative maxima
- Finding min and max of a function
- Maxima and minima
- Periodic table with phases
- Periodic relationships