Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 26

Topic

Radical Functions

Description

This example illustrates the function y = √(x + 1) - 1. The graph shows an increasing curve starting at (0, 0) and rising as x increases. A table lists x-values (0, -1, -3, -5, -7) with corresponding y-values (0, 0.414, 1, 1.449, and 1.828). Students are asked to create a table of x-y coordinates and graph the function.

This example introduces students to square root functions with a constant term inside and outside the radical. It helps them understand how these factors affect the shape of the graph and its vertical shift. By comparing this to previous examples, students can visualize how adding constants inside and outside the square root affects the function's behavior.

Providing multiple examples with different variations is essential for deepening students' 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.

Teacher's Script: Let's examine the function y = √(x + 1) - 1. How do you think this graph will compare to our previous examples? We'll use x-values of 0, -1, -3, -5, and -7. Notice how the y-values change as we plot these points. The curve starts at (0, 0) and rises more gradually than some of our earlier examples. Can anyone explain why this happens?

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