Worksheet 4: Graphs and One-Sided Limits

Teach collaboration and communication skills in addition to graphing logarithmic functions. Scholars in different groups graph different logarithmic functions by hand using provided coordinate points. These graphs provide the basis for...

With 30 problems, each accompanied by a blank graph, pupils get thorough practice solving systems of equations by graphing and finding the point of intersection. Answers are provided in coordinate form.

Discover how to find limits using graphs. Viewers learn how to determine limits of a piecewise function at specific points by analyzing a graph. They consider both one-sided and two-sided limits.

Do you want to play a little one-to-one? Learn to determine algebraically if a function is one-to-one. Work through two examples using the video as a guide. 

Functions are special relations, but are there special functions? A concept video defines a one-to-one function. Three problem videos cover examples in determining whether a relation is a function and whether it is a one-to-one...

One-to-one means the answer is simple, right? Given four graphs, pupils use a vertical line to test each graph to find out if they are one-to-one. By using the resource, learners realize that not all one-to-one relations are functions....

Not everything that's one-sided is bad. A slider interactive aids learners in investigating one-sided limits from graphs. A set of challenge questions assesses their understanding of the relationship between one- and two-sided limits.

A one-sided limit is no less important than a two-sided limit. Young mathematicians use an interactive to match limit notation to graphs. The exercise requires interpreting how one-sided limits connect to features of graphs.

Is the inverse of a function also a function? Pupils manipulate the graph of a function to view its inverse to answer this question. Using a horizontal and vertical line, class members determine whether the initial function is...

Investigate the definition of inverse functions graphically. Using the interactive, scholars create a graph of a function and view its resulting inverse. They then determine whether a group of functions have inverses that are also...