Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 13

Topic

Radical Functions

Description

This example illustrates the function y = √(-2x) + 1. The graph shows a decreasing curve with points marked at specific x-values (-7, -5, -3, -1, and 0). The table lists x-values (0, 1, 3, 5, and 7) with corresponding y-values of 1, 2.414, 3.449, 4.162, and 4.742. Students are asked to create a table of x-y coordinates and graph the function.

This example introduces students to square root functions with negative coefficients inside the radical. It helps them understand how these factors affect the direction and domain of the function. By comparing this to previous examples, students can see how the graph is reflected 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 = √(-2x) + 1. How do you think this graph will differ from our previous examples? We'll create a table of x-y coordinates using non-positive x-values: -7, -5, -3, -1, and 0. What happens to the y-values? When we plot these points, we see that our curve is decreasing. Can anyone explain why this is the case? 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.