We will begin our study of Inverse and Exponential functions on the blog.
* Apply direct and inverse variation functions to describe and solve problems involving physical laws of science.
* Create a table and scatterplot for a given set of data. Describe the independent/dependent variables, determine if the data set is afunction and whether it is continuous or discrete, and identify intervals that are increasing/decreasing. Use representations to make predictions and draw conclusions about the given set of data.
* Construct tables and graphs for a collection of real-world data. Determine a function that would best represent the data. Determine the regression equation for the data. Describe the strength of the regression equation as a predictor. Apply the representations to make and justify predictions and conclusions related to the data collection.
Key Understandings and Guiding Questions:
How can you distinguish between direct and inverse variation?
Direct variation involves multiplying a constant by the independent variable. Graphically direct variation is linear and is an increasing function.
Inverse variation involves dividing a constant by the independent variable. Graphically inverse variation is curved with asymptotes at the positive
y-axis and positive x-axis. and is a decreasing function.
What is the domain and range of a function and how does it differ from the domain and range of the problem situation?
The domain is the set of values of the independent variable, the x-values that "work" in the function.
The range is the set of values of the dependent variable, the y-values that we "get out" of the function.
For a function, the domain and range can be all real numbers, but in the problem situation, the domain and range may have to restricted to
values greater than or equal to zero.
How can you determine if a relation is a function?
If a relation is a function, each value of the independent variable will be associated with only one value of the dependent variable. As previously
discussed, the x's cannot be "floozies."
What is an asymptote and how does it appear in a graph of the function?
An asymptote is a line which the graph approaches as the independent or dependent variable gets very large in the positive or negative direction.
How can you determine if a function is increasing or decreasing over an interval?
If the graph goes up from left to right or if the x and y values both increase, the function is increasing for that interval.
If the graph goes down from left to right or the the x values increase and the y values decrease, the function is decreasing for that interval.
What methods of representations should be used to analyze a collection of data?
Tables, scatterplots, graphs, verbal descriptions, and algebraic representations.
How can the strength of the regression equation be determined?
The "r" value can be found using the graphing calculator. The closer the "r" value is to positive or negative 1, the better it is as a predictor.
To activate the "r" value on the graphing calculator, press 2nd > 0 and scroll down to "diagnostic on" and press enter.
If "r" is less than .33, there is a weak, very weak, to no correlation as it approaches 0.
If "r" is between .33 and .67, there is a moderate correlation.
If "r" is greater than .67, there is a strong, very strong, to perfect correlation at 1 or -1.
Click on the attachments below to view a video on inverse and exponential functions.