Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 32

Topic

Radical Functions

Description

This example demonstrates the function y = -√(2x) - 1. The graph shows a decreasing curve starting at (0, -1) and moving downward more steeply as x increases. A table lists x-values (0, 1, 3, 5, 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 builds on the previous one by introducing a coefficient inside the square root. It helps students understand how this coefficient affects the steepness of the graph while maintaining the negative square root and vertical shift. By comparing this function to y = -√(x) - 1, students can visualize the impact of the coefficient 2 on the function's behavior.

Providing a range of examples with different coefficients is essential for developing a deep understanding of square root functions. Each example challenges students to apply what they've learned in new contexts, fostering critical thinking and analytical skills. This approach helps students recognize patterns and relationships between equations and their graphs, preparing them for more complex mathematical concepts.

Teacher's Script: Now, let's look at the function y = -√(2x) - 1. How do you think this graph will compare to our previous example, y = -√(x) - 1? We'll use the same x-values: 0, 1, 3, 5, and 7. Notice how the y-values decrease more rapidly this time. When we plot these points, we can see that this curve starts at (0, -1) like the previous example, but falls more steeply. Can anyone explain why this happens? How does the coefficient 2 inside the square root affect the function?

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