Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 15

Topic

Radical Functions

Description

This example explores the function y = √(-0.5x) + 1. The graph shows a decreasing curve starting at (0, 1) and moving downward as x becomes more negative. A table lists x-values (0, -1, -3, -5, -7) with corresponding y-values of approximately 1, 1.707, 2.225, 2.581, and 2.871. Students are tasked with creating a table of x-y coordinates and graphing the function using these values.

This example introduces students to square root functions with a negative coefficient inside the radical and a constant term. It helps them understand how these factors affect the direction, steepness, and domain of the function. By comparing this to previous examples, students can see how the graph is reflected across the y-axis and how the domain is restricted to non-positive x-values.

Presenting a variety of examples is crucial for building a comprehensive understanding of square root functions. Each new example challenges students to apply their knowledge in a slightly different context, reinforcing their learning and helping them develop problem-solving skills. This approach encourages students to think critically about the relationship between equations and their graphical representations.

Teacher's Script: Let's examine the function y = √(-0.5x) + 1. How do you think this graph will differ from our previous examples? We'll use x-values of 0, -1, -3, -5, and -7. Notice how the y-values are increasing as x becomes more negative. When we plot these points, we see that our curve is decreasing but only exists for non-positive x-values. Can anyone explain why this happens? How does the negative coefficient inside the square root affect the function's behavior?

For a complete collection of math examples related to Radical Functions click on this link: Math Examples: Square Root Functions Collection.