Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 24

Topic

Radical Functions

Description

This example illustrates the function y = √(0.5x) - 1. The graph shows an increasing curve starting at (0, -1) and rising gradually as x increases. A table lists x-values (0, 1, 3, 5, 7) with their corresponding y-values (-1, -0.293, 0.225, 0.581, 0.871). Students are asked to create a table of x-y coordinates and graph the function, which includes these points.

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

Providing a range of examples with different coefficients and constants 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 are different. When we plot these points, we can see that this curve starts at (0, -1) like the previous example, but rises more slowly. Can anyone explain why this happens? How does the coefficient 0.5 inside the square root affect the function, and how is this different from having a coefficient of 2 or no coefficient at all?

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