Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 4

Topic

Radical Functions

Description

This example illustrates the function y = √(0.5x). The graph shows an increasing curve starting at the origin (0, 0) but rising more slowly than y = √(x). A table lists x-values (0, 1, 3, 5, and 7) with their corresponding y-values, which are smaller compared to previous examples in this series. Students are asked to create a table of x-y coordinates and graph the function y = √(0.5x), using x-values of 0, 1, 3, 5, and 7 with corresponding y-values of approximately 0.707, 1.225, 1.581, and 1.871.

This example introduces students to square root functions with fractional coefficients inside the radical. It helps them understand how coefficients less than 1 affect the shape of the graph, making it rise more slowly compared to y = sqrt(x). This comparison allows students to visualize the impact of different coefficients 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 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). How do you think this graph will compare to our first example, y = √(x)? We'll use the same x-values as before: 0, 1, 3, 5, and 7. Notice how the y-values are smaller this time. When we plot these points, we can see that this curve rises more slowly than y = √(x). 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.