Adding an exponent, sometimes referred to as a ‘power’, to the input variable of a linear function that passes through the origin creates a power function. Changing the parameters of these functions reveal some important and interesting patterns.
Tag: graphs
Quadratic Functions
What does each of the coefficients do? How does it change the graph of the parabola. What does a do, what does c do and a question still rarely asked, what does changing b do to change the graph. To see what b does more clearly we have you add a graph of the linear portion of the quadratic function to the picture so that you can see the pattern it makes and it causes the parabola to make. Quadratic functions give you a chance to really and experiment with this very important family of functions.
Solving Equations
Typical algebra courses start with equations and solving equations and then move to graphing and functions. We start with functions and use them to solve equations. We treat an equation as the equality of two functions, graph each one and then look at their intersection. This is a powerful way to think about solving equations due to Judah Schwartz and one that we believe will help many student to understand this algebra.
Linear Functions
Linear functions are the most important family of functions. They pervade our everyday lives and our work. Their graph is a line, and their general form is f(x)=mx+b where m is the slope of the function and b is the y-intercept, the value where the line crosses the y-axis. This Lab is designed to give you a picture of a linear function based on its formula. So play with it until you can picture the function from its formula and its formula from its graph.
Rate of Growth
We look at world population over the past 60+ years and ask whether the earth’s population is growing faster or slower today. Is it out of control and something we should all worry about or are we getting it under control? This is another problem directly related to climate change and one that students can argue with each other about. We use this opportunity to ask students about which kind of graph or chart would best convey the issue to other people. The type of graph or chart to be used to convey data is of great importance in business and industry today and one that requires students to creatively ask What if… about.