Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 34

Topic

Radical Functions

Description

This example illustrates the function y = -√(0.5x) - 1. The graph shows a decreasing curve starting at (0, -1) and moving downward gradually as x increases. A table lists x-values (0, 1, 3, 5, 7) with corresponding y-values of -1, -1.707, -2.225, -2.581, and -2.871. Students are asked to create a table of x-y coordinates and graph the function.

This example introduces students to square root functions with fractional coefficients inside the radical, along with a negative sign outside and a vertical shift. It helps them understand how coefficients less than 1 affect the shape of the graph, making it decrease more slowly compared to y = -sqrt(x) - 1. This comparison allows students to visualize the impact of different coefficients on the function's behavior while maintaining the negative square root and vertical shift.

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

Teacher's Script: Now, let's look at the function y = -√(0.5x) - 1. How do you think this graph will compare to our previous examples? We'll use the same x-values as before: 0, 1, 3, 5, and 7. Notice how the y-values decrease more slowly this time. When we plot these points, we can see that this curve starts at (0, -1) like the previous examples, but falls more gradually. Can anyone explain why this happens? How does the coefficient 0.5 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.